LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


ELECTROCHEMISTRY 

I 

THEORETICAL  ELECTROCHEMISTRY 

AND  ITS  PHYSICO-CHEMICAL 

FOUNDATIONS 


BY 

DR.    HEINRICH    DANNEEL 

Privatdozent  of  Physical  Chemistry  and  Electrochemistry  in  the 
Royal  Technical  High  School  of  Aachen 

TRANSLATED    FROM   THE   SAMMLUNG  GOSCHEN 
BY 

EDMUND   S.    MERRIAM,    PH.D. 

Associate  Professor  of  Chemistry  in  Marietta  College,  Ohio 


OF  THE 

UNIVERSITY 

OF 


FIRST    EDITION 
FIRST    THOUSAND 


NEW  YORK 

JOHN    WILEY    &    SONS 

LONDON:    CHAPMAN  &   HALL,    LIMITED 

1907 


SRAL' 


Copyright,  1907 

BY 
EDMUND  S.   MERRIAM 


55  3 


ROBERT   DRUMMONI),    PRINTER,    NEW    YORK 


INTRODUCTION. 


/  . 

THE  science  of  electrochemistry  has  come  to  have  a 
far  wider  range  of  application  than  formerly.  A  com- 
paratively short  time  ago  it  comprised  little  more  than 
methods  of  bringing  about  chemical  reactions  by  means 
of  electricity,  and  the  utilization  of  chemical  affinity  for 
the  production  of  an  electric  current.  It  has  now  become 
one  of  our  most  important  aids  in  the  investigation  of 
some  of  the  fundamental  problems  of  general  chemistry. 
The  measurement  of  electromotive  forces  is  the  safest, 
and  oftentimes  the  only,  means  of  determining  the  chem- 
ical force  with  which  reactions  take  place;  conductivity 
measurements  have  given  us  an  insight  into  the  nature  of 
solutions;  electrochemistry  has  given  rise  to  one  of  the 
most  fruitful  of  the  modern  chemical  theories,  the  theory 
of  electrolytic  dissociation. 

In  practical  as  well  as  theoretical  line's  electrochemistry 
has  been  of  immense  value.  Aside  from  the  fact  that 
many  substances,  such  as  the  alkali  metals,  aluminium, 
magnesium,  calcium  carbide,  etc.,  which  can  only  be 
made  with  the  greatest  difficulty  by  purely  chemical 
means,  are  easily  manufactured  with  the  help  of  elec- 
tricity, let  us  remember  that  electrochemistry  gives  us  ' 

1 6232:5  ia 


iv  INTRODUCTION. 

a  nearly  perfect  means  of  utilizing  the  enormous  power 
of  our  waterfalls  for  chemical  purposes,  and  enables 
us  to  store  up  and  transport  this  energy  which  we  receive 
from  the  sun.  Finally  electrochemistry  gives  us  many 
compounds  in  a  quicker,  and  therefore  cheaper,  way 
than  the  old  purely  chemical  processes. 

Theoretical,  or  general  chemistry,  and  electrochemistry 
are  not  separable;  comprehension  of  one  presupposes 
knowledge  of  the  other.  Therefore  before  we  take  up 
electrochemistry  proper  we  will  go  over  some  of  the 
physical  and  physico-chemical  principles  which  form 
the  basis  of  our  present  ideas  in  the  field  of  electro- 
chemistry. We  will  then  discuss  the  various  theories  of 
electrochemistry  and  give  such  illustrations  as  are  nec- 
essary for  their  better  comprehension.  Experimental 
results  and  their  applications,  as  well  as  methods  of 
measurement,  etc.,  will  be  contained  in  the  second  volume. 
The  third  will  be  devoted  to  the  technical  applications. 


TABLE  OF  CONTENTS. 


PAGE 

INTRODUCTION iii 

CHAPTER  I. 

WORK,  CURRENT,  AND  VOLTAGE.  , i 

Kinds  of  Energy,  and  Their  Relationships.  Work  Done  by 
Natural  Processes.  Principles  of  Thermodynamics.  Maximum 
Work  and  Free  Energy;  Determination  of  Same.  Reversibility. 
Reaction  Velocity  and  Chemical  Force.  Ohm's  Law.  Catalysis. 
Gas  Laws,  and  the  Performance  of  Work  by  the  Expansion  of 
Gases.  Osmotic  Pressure,  and  Osmotic  Work.  Semi-permeable 
Walls.  Plant  Cells,  Quantitative  Measurements.  Work  from 
Osmotic  Pressure.  Calculation  of  Chemical  Work  from  Osmotic 
Pressure  and  van't  Hoff's  Equation. 

CHAPTER  II. 

CHEMICAL  EQUILIBRIUM,  STATICS,  AND  KINETICS 32 

Complete  and  Incomplete  Reactions.  Equilibrium.  Law  of 
Mass  Action.  Laws  of  Chemical  Kinetics  and  Statics.  Active 
Mass.  Dissociation  of  Gases.  CO  and  Os-  Homogeneous  and 
Heterogeneous  Systems.  Solution  of  Salts  and  Vapor  Pressure. 
Change  of  Equilibrium  with  the  Temperature.  CO+O2.  van't 
Hoff's  Equation. 

CHAPTER  III. 

THEORY  OF  ELECTROLYTIC  DISSOCIATION 45 

Freezing-point,  Boiling-point,  and  Osmotic  Pressure  of  Solu- 
tions. Dissociation.  History  of  Electrochemistry,  with  the 
Dissociation  Theory  and  its  Basis.  Faraday,  Grotthus,  Clausius, 


VI  TABLE   OF  CONTENTS. 

PAGE 

Hittorf,  van't  Hoff,  Arrhenius.  Degree  of  Dissociation  (Table) , 
Law  of  Mass  Action.  Applications  of  the  Theory  in  Chemistry. 
Precipitation.  Dissociation  by  Steps.  Ions  and  the  Dissocia- 
tion Constant  of  Water.  Neutralization.  Hydrolysis.  Sapon- 
ification.  Table  of  Dissociation  of  Water.  Additive  Properties. 
Physiological  Applications. 

CHAPTER  IV. 

CONDUCTIVITY 77 

Ohm's  Law.  Specific  Conductivity.  Temperature  Coeffi- 
cient. Metallic  and  Electrolytic  Conductivity.  Conductivity  of 
Solutions.  Charge  on  the  Ions.  Velocity  of  the  Ions.  Equiva- 
lent Conductivity.  Conductivity  of  the  Ions  and  Their  Inde- 
pendent "Wandering."  Water.  Sulphuric  Acid.  Dissociating 
Power  (Table).  Strength  of  Acids  and  Bases.  Distribution. 
Sugar  Inversion.  Decomposition  of  Ethereal  Salts.  Dissociation 
Constant  and  Ostwald's  Dilution  Law.  Isohydric  Solutions. 
Enforced  Lowering  of  Dissociation  and  Solubility  Product.  Dis- 
sociation by  Steps.  Conductivity  and  Temperature.  Measure- 
ment of  the  Transport  Number.  Absolute  Ionic  Velocities. 
Dielectric  Constant. 

CHAPTER  V. 

ELECTROMOTIVE  FORCE  AND  THE  GALVANIC  CURRENT 115 

Difference  of  Potential.  Contact  Electricity.  Galvanism. 
Galvani,  Volta,  Daniell.  Calculation  of  Electromotive  Forces. 
Reversibility.  Gibbs-Helmholtz  Formula,  and  van't  Hoff's 
Equation.  Nernst's  Formula.  Fugacity.  Solution  Pressure. 
Electrolytic  Potential.  Daniell  Cell.  Gas  Electrodes.  Poten- 
tial of  Alloys.  Potential  of  Compounds.  Electrodes  of  tHe 
Second  Kind.  Oxidation  and  Reduction  Potential.  Concen- 
tration Cells.  Diffusion  Cells.  Applications  of  Nernst's  For- 
mula. Solubility.  Neutralization  Cells.  Secondary  Elements, 
and  the  Accumulator. 

CHAPTER  VI. 

POLARIZATION  AND  ELECTROLYSIS 151 

Polarization.  Polarization  Capacity.  Electrolysis  of  Water, 
Residual  Current.  Decomposition  and  Deposition  Voltages. 


TABLE  OF  CONTENTS.  Vll 

PAGB 

Overvoltage.  Electrolysis  of  Mixtures.  Faraday's  Law.  Table 
of  Atomic  and  Equivalent  Weights.  Electrolysis.  Secondary 
Reactions. 

CHAPTER  VII. 

ELECTRON  THEORY 169 

LITERATURE 173 

INDEX. *77 


OF  THE 

f    UNIVERSITY  ) 

OF 
sf^L'fORNVhs 


ELECTROCHEMISTRY, 


CHAPTER  I. 

WORK,  CURRENT,  AND  VOLTAGE. 

THE  most  important  question  ior  scientific  and  technical 
progress  is,  How  much  work  can  a  given  chemical 
reaction  perform  ?  This  question  is  of  equal  or  perhaps 
greater  importance  than  the  question  as  to  what  happens 
when  two  substances  are  brought  together.  If  we  know 
the  work  which  a  certain  reaction  can  do,  for  instance 
the  reaction  CO  +  O  =  CO2,  and  the  temperature  co- 
efficient of  its  ability  to  do  work,  we  know  at  once  whether 
or  not  the  reaction  occurs  and  the  conditions  necessary 
for  its  occurrence.  We  see  from  the  value  of  the  energy, 
that  this  reaction,  the  oxidation  of  carbon  monoxide, 
takes  place  at  ordinary  temperatures  with  great  violence, 
in  fact  explosively;  further,  that  the  reaction  is  less 
complete  the  higher  the  temperature,  and  that  at  very 
high  temperatures  it  even  goes  in  the  opposite  direction; 
i.e.,  carbon  monoxide  not  only  will  not  burn,  but  carbon 
dioxide  is  decomposed  into  carbon  monoxide  and  oxygen. 

We   can   distinguish    six   different   kinds   of    energy: 


2  ELECTROCHEMISTRY. 

i,  mechanical  energy;  2,  volume  energy;  3,  chemical 
energy;  4,  electrical  energy;  5,  heat  energy,  and  6, 
radiant  energy.  These  different  forms  of  energy  are 
mutually  transformable  and  if  we  have  a  suitable  mechan- 
ism, the  transformation  is  quantitative.  Heat  energy 
forms  an  exception  to  this  rule ;  the  complete  transforma- 
tion of  heat  into  electrical  or  mechanical  energy  is  theo- 
retically and  practically  impossible,  although  mechanical 
or  electrical  energy  may  be  completely  transformed  into 
heat. 

The  scientific  unit  of  mechanical  work  is  the  erg 
(  =  i  dyne  X  i  centimetre)  and  this  is  the  unit  of  the 
so-called  C.G.S.  system.  The  practical  unit  is  the 
kilogram-metre,  which  is  the  work  necessary  to  raise  1000 
grams  through  a  height  of  100  centimetres,  or  the  work 
which  a  kilogram  can  do  in  falling  a  distance  of  i  metre. 

A  kilogram  weight  (not  to  be  confused  with  the  mass  of 
a  kilogram)  is  the  force  with  which  the  mass  of  i  kilogram 
(  =  i  litre  of  water  at  4°  C.)  is  attracted  by  the  earth.  A 
falling  body  attains  as  a  result  of  the  earth's  attraction  an 
acceleration  of  980.6  cms.  per  second,  so  that  a  gram 
weight  represents  a  force  of  980.6  dynes.  The  unit  of 
force  =  i  dyne  is  that  force  which,  acting  on  the  mass 
of  i  gram,  gives  it  an  acceleration  of  i  cm.  per  second. 
Acceleration  is  the  increase  of  velocity  per  second. 

distance 
Velocity  =  ~. — — .     A  kilogram-metre  is  100000  times 

as  great  as  a  gram-centimetre,  i.e.,  =  98  060  ooo  ergs. 

The  unit  of  volume  energy  is  the  litre-atmosphere. 
When  any  body,  for  instance  a  gas,  which  always  exerts 
a  pressure  on  the  walls  of  the  vessel  enclosing  it  (cf.  p.  16) 
expands,  the  weight  of  the  atmosphere  above  it  is  dis- 


WORK,   CURRENT,  AND   VOLTAGE.  3 

placed  by  an  amount  corresponding  to  the  number  of 
litres  of  expansion  of  the  gas.  The  expanding  gas 
therefore  does  work  against  the  pressure  of  the  atmosphere. 
(In  general,  every  increase  of  volume  taking  place  against 
a  pressure,  or  every  contraction  brought  about  by  a  pres- 
sure, is  accompanied  by  a  gain  or  loss  of  work.)  In  the 
barometer  the  pressure  of  the  atmosphere  forces  a  column 
of  mercury  i  sq.  cm.  in  cross-section  up  to  a  height  of  76 
cms.  Such  a  column  of  mercury  weighs  1.0333  kilograms, 
since  the  specific  gravity  of  mercury  is  13.596.  The 
pressure  of  one  atmosphere  therefore  is  1.0333  kg.  per 
sq.  cm.,  or  103.33  kg.  per  sq.  decimetre.  If  then  103.33 
kilograms  are  raised  i  decimetre,  i.e.,  if  a  body  expands 
by  i  litre,  the  work  done  is  the  same  as  when  i  gram 
is  raised  i  033  ooo  cms.  i  gr.  cm.  =  980.6  ergs;  the  value 
of  i  litre  atmosphere  is  therefore  980.6X1033000  = 
i  013  200000  ergs. 

The  ordinary  unit  of  electric  work  is  the  watt-second. 
Watt  is  the  "power"  of  an  electric  current  of  i  ampere 
under  the  pressure  of  i  volt.  By  power  is  meant  the 
work  done  in  unit  time,  i.e.,=  work/time.  An  ampere 
is  the  amount  of  electricity  measured  in  coulombs 
flowing  through  a  conductor  in  unit  time.  A  coulomb 
is  the  unit  quantity  of  electricity.  A  coulomb  in  passing 
through  a  silver  voltameter  precipitates  0.001118  gr. 
of  silver;  a  coulomb  is  the  electric  charge  (cf.  p.  53)  on 
0.01036  milligram  equivalents  of  every  ion  and  will 
precipitate  this  quantity  of  any  ion  on  an  electrode.  A 
current  of  i  ampere  flows  through  a  conductor  when  the 
quantity  of  electricity  passing  is  i  coulomb  per  second. 
An  ampere  is  the  tenth  part  of  the  unit  of  current  in  the 
C.G.S.  system. 


4  ELECTROCHEMISTRY. 

Electric  pressure  or  difference  of  potential  is  ordinarily 
measured  in  volts.  A  volt  is  that  pressure  which  suffices 
to  send  a  current  of  i  ampere  through  a  resistance  of  i 
ohm  (legal  definition).  One  volt  is  equal  to  io8  C.G.S. 
units.  A  Daniell  cell  has  an  electromotive  force  or 
difference  of  potential  of  i.i  volts;  a  storage  battery 
has  2.0  volts.  A  watt  is  i  voltXi  ampere  (a  power), 
and  a  watt-second  is  the  work  which  a  current  of  i  ampere 
is  able  to  do  when  flowing  for  i  second  through  a  resistance 
of  i  ohm.  A  watt-second  is  therefore  io8Xio~1  =  io7 
ergs. 

Heat  energy  is  measured  in  calories.  A  calorie  is  the 
quantity  of  heat  which  is  necessary  to  raise  the  temperature 
of  i  gram  of  water  from  15°  C.  to  16°  C.  Since  the 
specific  heat  of  water  is  not  independent  of  the  tempera- 
ture, the  quantity  of  heat  necessary  to  raise  the  tem- 
perature of  i  gr.  of  water  i°  C.  is  different  at  different 
temperatures.* 

The  mechanical  equivalent  of  heat  has  been  determined 
by  many  investigators;  we  will  use  the  value  adopted  by 
Nernst,f  42  600.  The  meaning  of  this  number  is  as 
follows :  If  i  gram  falls  42  600  centimetres,  or  if  i  kg.  falls 
42.6  cms.  and  the  total  kinetic  energy  (vis  viva)  of  the 
falling  weight  is  converted  by  impact  into  heat,  this 
quantity  of  heat  is  just  sufficient  to  raise  the  temperature 
of  i  gram  of  water  from  15°  C.  to  16°  C.,  i.e.,  one  calorie 


*  Beside  the  above-defined  calorie,  which  is  the  one  most  generally 
in  use,  there  are  the  "mean  calorie "  =  T^7  the  quantity  of  heat  neces- 
sary to  warm  i  gr.  of  water  from  o°  to  100°,  and  the  "zero-point 
calorie,"  the  quantity  of  heat  necessary  to  warm  i  gr.  of  water  from 
o°  to  i°.  The  "kilogram  calorie"  is  1000  times  the  15°  calorie. 

f  Theoretische  Chemie,  p.  12.     Enke,  Stuttgart. 


WORK,   CURRENT,  AND   VOLTAGE.  5 

is  evolved.  The  energy  of  the  i  gram  weight  is  then 
42  600X980. 6  =  41  777  ooo  ergs  (980.6  is  the  acceleration 
due  to  gravity). 

There  is  no  fixed  unit  for  chemical  energy,  it  is  generally 
measured  in  volt  coulombs.  As  yet  there  is  also  no 
common  unit  for  radiant  energy. 

With  the  help  of  the  following  table  *  it  is  easy  to 
express  a  given  quantity  of  work  in  any  of  the  different 
units. 


Absolute 
Units, 
Ergs 

Electrical 
Units, 
Watt-seconds 

Heat- 
units, 
Gr.  Calories 

erg 
watt-second               = 
gr.  calorie 
litre-atmosphere        = 
kg.-metre 
horse-power-second  = 
Gas  constant  R 

I 

I07 

4.187X10' 
i.oi3X  io9 
9.806X10' 
7-  355Xio9 
8.  3155X10' 

io-7 

4.189 

0.01013 

9.806 

735-5 
8.3155 

2.387XIO-8 
0.2387 
i 
24.19 
2.341 
I75-58 
1.985- 

Litre- 
atmospheres 

Kilogram- 
metres 

Horse-power- 
seconds 

i  erg 
i-  watt-second 
i  gr.  calorie                   = 
i  litre-atmosphere        = 
i  kg.-metre 
i  horse-power-second  = 
Gas  constant  R 

9.86QXIO-10 
o  .  009869 
0.041342 
I 
0.09678 

7-2585 

0.0821 

I.OI98X-IO-8 
o.  10198 
0.4272 

IO-333 

i 
75.00 
0.848 

i.3597Xio-10 
0.0013597 
0.005696 
0.13778 
0.01333 

0.011308 

From  the  foregoing  it  is  clear  that  an  expression  de- 
noting work  is  always  made  up  of  two  factors.  A  summary 
of  these  will  perhaps  be  of  use  in  making  the  relationship 
clearer. 


*  Table  of  H.  Steinwehr,  recalculated  after  Nernst,  Zeitschr.  f.  Elec- 
trochemie,  io,  629,  1904. 


ELECTROCHEM1S  TRY. 


Mechanical  work: 
Velocity 

Acceleration 

Force 
Work 

Power 
Work 

Weight 

Work  of  expansion 

Pressure 
Electrical  work 

Current  strength 


Distance 
Time   * 
Increase  of  velocity 

Time 

=  Acceleration  X  mass. 
=  Force  X  distance. 

Work 
"  Time' 

=  Mass  X  length  of  fall  X  accelera- 
tion due  to  gravity. 
=  Mass   X   acceleration     due     to 

gravity. 

=  Increase  of  volume  X  pressure. 
Weight 
Surface  * 

=  Voltage  X  coulombs. 
Coulombs 


Electrical  power 
Chemical  work 


Time 

=  Voltage  X  current. 
=  Chemical  potential  X  quantity  of 

substance. 

The  conceptions  of  chemical  and  electric  potential 
will  occur  repeatedly  and  will  be  explained  in  their  proper 
place. 

Work  Done  by  Natural  Processes. 

Fundamental  Law. — A II  processes  in  Nature  whtch  take 
place  of  themselves  can  famish  work,  and  only  such  proc- 
esses occur  spontaneously,  which,  ivith  the  aid  of  suitable 
apparatus,  can  be  made  to  perform  work.  Among  such 
processes  are  the  union  of  electric  charges;  movements 


WORK,   CURRENT,  AND   VOLTAGE.  ^ 

of  liquid  from  a  higher  to  a  lower  level;  all  movements 
of  masses  in  general  which  occur  spontaneously;  further, 
chemical  reactions;  equalization  of  different  tempera- 
tures, etc. 

The  most  important  question  for  us  is,  how  much 
work  we  can  obtain  from  a  given  process  under  the  most 
favorable  conditions,  the  so-called  " maximum  work." 
In  order  to  appreciate  the  meaning  of  this  term  we  must 
review  two  laws  concerning  the  relation  between  heat  and 
work,  the  two  principles  of  thermodynamics. 

First  Law,  Principle  of  the  Conservation  of  Energy.— 
Just  as  no  substance  can  be  created  from  nothing  nor  be 
absolutely  destroyed  (law  of  the  conservation  of  matter), 
so  energy  can  neither  be  created  from  nothing  nor  anni- 
hilated. "Perpetual  motion,"  i.e.,  a  machine  which 
continually  does  work  without  having  energy  given  to  it 
in  any  way,  is  scientifically  an  absurdity.  Many  inventors 
who  have  had  such  an  end  in  view  have  tried  to  achieve 
the  impossible. 

A  few  illustrations  will  make  the  meaning  of  this  law 
clear. 

We  lift  a  weight  of  10  kg.  vertically  from  the  floor 
through  a  distance  of  i  metre.  In  so  doing  our  muscles 
do  10  kg.  metres  of  work.  The  weight  has  now  a  capacity 
for  doing  work,  or  potential  energy,  of  10  kg.  metres,  if 
we  disregard  the  energy  it  may  have  had  to  start  with.  If 
we  let  the  weight  fall  again  it  attains  as  a  result  of  the 
earth's  attraction  a  certain  "vis  viva"  (the  potential 
energy  changes  to  kinetic  energy)  and  when  it  strikes  the 
floor  this  energy  is  converted  into  heat.  If  we  measure 
the  heat  we  find  it  to  be  23.5  calories,  and  this,  as  we  see 
from  the  table  on  p.  5,  is  just  equal  to  the  original 


8  ELECTROCHEMISTRY. 

10  kg.  metres  we  spent  in  raising  the  weight.  If  we 
denote  by  U  the  change  in  energy  resulting  from  the  fall 
(in  this  case  10  kg.  metres)  and  by  W  the  heat  generated 
by  the  impact  of  the  weight  on  the  floor,  then 

U  =  W. 

We  now  tie  to  the  falling  weight  a  cord,  lead  it  over 
a  pulley,  and  fasten  a  9  kg.  weight  to  the  other  end,  so 
that  this  last  is  raised  a  metre  by  the  fall  of  the  first; 
let  the  work  necessary  to  raise  this  weight  be  A  (in  this 
case  9  kg.  metres).  We  will  now  find  that  the  heat 
developed  by  the  impact  of  the  first  weight  on  the  floor  is 
2.35  calories;  if  we  denote  this  by  W,  then 

U=A+W. 

If  we  supply  extra  work  to  the  process — for  instance,  by 
accelerating  either  the  10  or  9  kg.  weight  by  a  blow — this 
work  A'  must  also  appear  in  the  heat  developed, 

W=U-A+A'. 

In  every  case  the  change  in  the  total  energy  plus  the 
heat  expended  and  work  expended  is  equal  to  the  work 
obtained  plus  the  heat  obtained. 

If  we  let  a  chemical  reaction  take  place  in  such  a  way 
that  no  work  is  done,  we  obtain  the  change  in  total 
energy  as  heat,  which  in  this  case  we  call  the  "heat  of 
reaction"  (Warmetonung).  In  the  combustion  of  coal 
we  obtain  with  the  help  of  a  steam-boiler  only  about 
20%  of  the  heat  of  reaction  as  mechanical  energy;  the 
other  80%  goes  over  into  heat  which  is  lost  up  the  chimney 
and  by  radiation.  If  we  obtain  more  work  than  that 


WORK,   CURRENT,  AND   VOLTAGE.  9 

which  corresponds  to  the  heat  of  reaction  (which  is 
possible  in  some  cases)  the  extra  heat  must  be  supplied 
by  the  surroundings,  i.e.,  the  reaction  mixture  cools 
itself  off. 

Second  Law,  Principle  of  the  Transformation  of  En- 
ergy.— We  wish,  of  course,  to  know  how  much  work 
we  can  get  out  of  a  given  process  under  the  most  favorable 
conditions,  i.e.,  what  the  maximum  work  is.  Thomson, 
and  after  him  Berthelot,  proposed  the  law  (principe  du 
travail  maximum)  that  the  maximum  work  may  be 
calculated  from  the  heat  of  reaction,  and  that  the  two  are 
equal.  Helmholtz,*  however,  later  proved  that  this  is 
not  the  case. 

The.  basis  of  Helmholtz's  theory  is  the  well-known 
fact  that  heat  can  do  no  work  when  it  is  at  rest.  Just  as 
water  can  do  no  work  when  it  is  at  rest  and  only  does  so 
when  it  falls  from  a  higher  to  a  lower  level,  and  just  as 
electricity  can  only  perform  work  as  it  falls  from  a  higher 
to  a  lower  potential,  so  heat  will  only  do  work  when  it 
falls  from  a  higher  to  a  lower  temperature/ 
•  If  heat  is  to  be  converted  into  work  we  must  have 
differences  of  temperature.  To  cite  an  illustration  of 
Nernst's,  we  cannot  utilize  the  enormous  reservoir  of 
heat  in  the  sea  to  turn  the  propellers  of  the  ocean  steamers. 
One  might  conceive  of  the  ships'  engines  taking  heat  from 
the  ocean  water,  using  it  in  the  performance  of  work, 
i.e.,  in  propelling  the  ship,  and  then  returning  it  to  the 
water  in  the  form  of  friction.  Experience  shows  that 
such  a  machine,  which  would  not  contradict  the  law  of  the 

*  Thomson  has  accepted  the  views  of  Helmholtz,  but  Berthelot  and 
many  of  the  French  scientists  still  cling  to  the  principe  du  travail  maxi- 
mum although  it  has  been  clearly  shown  to  be  incorrect. 


10  ELECTROCHEMISTRY. 

conservation  of  energy,  is  unfortunately  an  impossibility; 
such  a  machine,  however,  has  received  the  name  of 
"perpetual  motion  of  the  second  kind." 

By  a  simple  thermodynamic  cycle  it  can  be  shown 
that  when  an  amount  of  heat  Q  at  the  absolute  tempera- 
ture *  T  falls  to  the  temperature  T-dT*  in  the  most 
favorable  case  the  quantity  of  work  dA  to  be  obtained  is 


By  combining  this  equation  with  the  equation  U=A+W 
(cf  .  p.  8)  we  have 


~-^p  is,  however,  nothing  else  than  the  temperature  co- 

efficient of  the  capacity  for  doing  work,  i.e.,  it  is  the 
amount  by  which  A  changes  when  the  temperature  is 
changed  one  degree.  If  we  represent  the  temperature 
coefficient  by  a,  then 

A-aT=U. 

The  formula  A  —  U=T-^  is  the  exact  expression  in  one 
equation  of  both  laws  of  thermodynamics. 

*  The  gas  laws  make  it  probable  that  there  can  be  no  temperature 
lower  than  —273°  C.  —273  is  therefore  called  the  absolute  zero  of 
temperature.  Temperatures  counted  from  the  absolute  zero  are  de- 
noted by  T;  if  /  is  the  ordinary  Celsius  temperature,  counted  from  the 
freezing-point  of  water,  T=*  273  -H. 

f  An  infinitely  small  value,  which  is  not  zero,  but  approaches  zero, 
is  denoted  by  a  prefixed  d.  dQ  is  an  infinitely  small  quantity  of  heat, 
dU  an  infinitely  small  change  of  total  energy,  etc. 


WORK,  CURRENT,  AND   VOLTAGE.  II 

From  this  equation  we  can  derive  several  very  important 
results:  i.  The  change  in  total  energy  U,  which  in 
chemical  reactions  is  simply  the  heat  of  reaction,  is  only 
equal  to  the  work  obtainable,  or,  as  it  is  often  called,  the 
"free  energy,"  when  the  free  energy  is  independent  of 
the  temperature,  i.e.,  when  a  =  o.  2.  At  the  absolute 
zero  (  —  273°  C.)  A  is  always=Z7.  3.  If  a  is  positive, 
i.e.,  if  the  free  energy  increases  when  the  temperature  is 
raised,  we  may  obtain  more  work  than  corresponds  to 
the  heat  of  the  reaction.  The  excess  must  be  supplied  by 
the  surroundings,  and  the  reaction  mixture  cools  itself  off. 
This  happens,  of  course,  only  when  we  do  extract  the 
maximum  work.  4.  If  a  is  negative,  excess  heat  results, 
and  the  system  becomes  warm,  even  when  the  maximum 
work  is  obtained.  With  the  exception  of  No.  2,  all 
these  cases  are  realized. 

The  Daniell  cell  furnishes  a  good  illustration  of  these 
points.  This  affords  electric  energy  as  the  result  of  the 
following  equation: 

Zn  +  CuSO4  =  ZnSO4  +  Cu, 

i.e.,  copper  is  precipitated  from  a  solution  of  CuSC>4  by 
zinc.  A  Daniell  cell  in  using  up  32.7  grs.  of  zinc  gives 
at  o°  C.  electric  energy  equivalent  to  25  263  calories; 
electrical  measurements  further  show  that  the  free  energy 
increases  0.786  calorie  per  degree  rise  of  temperature. 
/.  aT  =  0.786X273  =  213  calories.  The  heat  of  reaction 
is  therefore 

£/  =  25  263-213  =  25  050  cal. 

Calorimetric  measurements  gave  25  055  calories,  in 
excellent  agreement  with  the  calculated  value. 


12  ELECTROCHEMISTRY. 

The  questions  now  arise,  How  do  we  determine  the 
maximum  work?  or,  How  can  we  compel  a  reaction 
to  do  its  best?  To  do  this  we  must  contrive  an 
arrangement  which  converts  chemical  into  mechanical 
or  electrical  energy,  and  which  works  so  perfectly  that 
there  are  no  losses  due  to  secondary  causes,  such  as 
leakage,  friction,  radiation,  etc.  Further,  the  reaction 
must  take  place  in  such  a  manner  that  we  may  stop  it  at 
any  time,  and  by  putting  back  exactly  the  same  amount 
of  work  we  have  already  obtained  from  it,  bring  the 
system  to  its  original  condition.  Such  a  process  is  called 
a  "reversible"  one.  Absolute  reversibility  would  be 
possible  experimentally  only  if  we  ourselves  were  perfect 
beings;  since,  unfortunately,  even  electrochemists  can 
make  no  such  claim,  we  must  content  ourselves  with 
approaching  the  above  requirements  of  reversibility  as 
closely  as  possible.  An  arrangement  which  fulfils  these 
requirements  very  perfectly  is  the  galvanic  cell  (battery). 
In  it  reactions  often  take  place  with  practically  perfect 
reversibility,  and  for  this  reason  the  scientific  chemist 
should  realize  the  importance  of  electrochemistry. 

The  work  which  a  reaction  can  do  is  the  point  which 
has  a  special  interest  for  us.  One  of  the  chief  aims  of 
electrochemistry  is  to  obtain  work  from  chemical  reactions, 
such,  for  instance,  as  the  combustion  of  coal;  the  reaction 
between  zinc  and  copper  sulphate  or  between  lead,  lead 
peroxide,  and  sulphuric  acid.  Another  aim  is  the  com- 
pulsion of  chemical  reactions  by  means  of  electrical  work, 
as  in  the  manufacture  of  aluminium  from  its  oxide,  or 
the  preparation  of  bleaching  solutions  from  common  salt. 
In  the  first  case  we  are  satisfied  when  we  know  the 
maximum  work  which  the  given  reaction  can  do;  in  the 


WORK,   CURRENT,   AND   YOLTAGE.  13 

second  we  must  learn  the  maximum  work  of  the  reverse 
reaction. 

If  we  have  a  solution  in  which  two  reactions  may  take 
place,  for  instance  a  solution  of  FeSC>4  and  CuSC>4,  and 
wish  to  obtain  the  copper  electrolytically,  we  must  know 
which  of  the  two  reactions  takes  place  easier;  i.e.,  how 
much  work  is  sufficient  to  precipitate  the  copper  on  the 
cathode,  but  does  not  suffice  to  precipitate  the  iron.  In 
other  words,  we  must  know  the  work  necessary  for  each 
reaction. 

If  we  know  the  maximum  work  of  a  reaction  we  know 
also,  as  already  stated,  whether  it  will  take  place  of  itself 
or  not.  If  we  know,  for  instance,  that  the  displacement 
of  copper  by  zinc  according  to  the  equation  Zn  +  CuSC>4  = 
Cu  +  ZnSO4  can  perform  work,  we  know  from  this  fact 
that  the  reaction  will  go  on  of  its  own  accord,  and  that 
therefore  the  reverse  reaction  which  requires  the  ex- 
penditure of  work  will  not  occur  spontaneously;  that  is, 
zinc  cannot  be  precipitated  by  copper  from  a  zinc  salt 
solution. 

Another  example  is  the  following:  When  we  dissolve 
hydrogen  peroxide  in  water  we  observe  no  reaction; 
decomposition  according  to  the  equation  H2O2=H2O  +  O 
apparently  does  not  take  place  of  itself.  It  would  there- 
fore appear  probable  that  the  reverse  reaction  would  occur 
spontaneously.  However,  if  we  pass  oxygen  gas  into 
water,  H2O2  is  not  formed  in  measurable  amounts. 
Accordingly  the  only  way  of  deciding  which  of  the  two 
reactions,  decomposition  or  formation,  is  spontaneous, 
is  to  measure  the  work  involved.  It  is  found  that  work  is 
necessary  for  the  formation  of  H2O2;  work  can  be  done  by 
its  decomposition  and  therefore  this  reaction  goes  on  of 


14  ELECTROCHEMISTRY. 

itself.  A  similar  case  is  found  in  detonating  gas.  Hydro- 
gen and  oxygen  may  be  kept  together  many  years  without 
the  visible  formation  of  water.  In  this  case,  also,  the  only 
means  of  determining  which  reaction  is  spontaneous  is 
by  measuring  the  work.  The  reason  why  we  do  not 
observe  either  a  decomposition  of  the  H2O2  or  a  formation 
of  H2O  lies  in  the  slowness  of  the  reaction. 

Reaction  Velocity  and  Chemical  Force. 

At  the  end  of  the  last  paragraph  mention  was  made  of 
the  slowness  of  a  reaction,  and  we  must  now  see  what 
bearing  the  reaction  velocity  has  on  the  work  of  a  process. 
In  utilizing  a  chemical  reaction  for  the  production  of 
work  the  first  point  to  be  considered  is  the  speed  with 
which  the  reaction  proceeds.  A  reaction  which  can 
furnish  a  million  kg. -metres  can  be  of  no  use  to  us  if  it 
requires  a  milliard  years  before  it  is  completed,  nor,  on 
the  other  hand,  if  it  only  requires  a  fraction  of  a  second, 
for  our  machines  are  too  imperfect  to  take  care  of  such  a 
power,  and  the  greater  part  would  be  lost  in  the  form 
of  heat.  The  reaction  2H2+O2  =  2H2O  at  ordinary 
temperatures  goes  too  slow,  and  at  high  temperatures, 
too  fast  (explosively).  An  electrochemical  arrangement, 
however,  enables  us  to  regulate  the  velocity  within  certain 
limits,  and  so  quantitatively  obtain  the  work  of  the  re- 
action. 

A  law  similar  to  Ohm's  law  regulates  the  velocity  of 
chemical  reactions. 

impelling  force 

Reaction  velocity =—. — -. — ,       . —    — . 
chemical  resistance 

We  can  always  calculate  the  impelling  force  from  the 


WORK,   CURRENT,  AND   VOLTAGE.  15 

work  which  the  given  reaction  can  do,  but  we  know  very 
little  about  chemical  resistance.  In  most  reactions,  prob- 
ably in  all,  the  chemical  resistance  increases  as  the  tem- 
perature decreases,  and  would  appear  to  become  infinite 
at  the  absolute  zero,  where  all  chemical  action  would 
cease.  In  many  cases  we  can  reduce  the  chemical 
resistance;  this  may  be  done,  for  example,  in  the  case  of 
H2O  formation  by  constructing  a  gas  cell.  The  chemical 
resistance  is  also  lowered  by  raising  the  temperature,  or 
by  bringing  finely  divided  platinum  into  the  gas  mixture. 
The  platinum  does  not  take  a  visible  part  in  the  reaction, 
for  it  is  the  same  after  the  reaction  as  before.  But  by 
the  simple  presence  of  platinum  we  can  increase  the 
reaction  velocity  at  ordinary  temperatures  till  explosion 
occurs.  Such  substances  which  diminish  chemical  re- 
sistance are  known  as  catalytic  agents  or  catalyzers. 
Their  presence  changes  neither  the  impelling  force  nor 
the  nature  of  the  reaction.  In  technical  work  there  are 
many  reactions  which,  were  it  not  for  suitable  catalyzers, 
would  go  so  slowly  as  to  be  commercially  worthless.  We 
need  only  mention  the  " contact  process"  for  sulphuric 
acid,  in  which  a  number  of  catalyzers  have  found  appli- 
cation in  bringing  about  the  union  of  sulphur  dioxide  and 
oxygen.* 

*  The  reader  will  find  a  collection  of  the  most  important  technical 
reactions  in  which  catalysis  plays  an  important  part  in  an  address 
of  Bodlander's,  delivered  before  the  Berlin  International  Chemical 
Congress,  which  has  appeared  with  other  collections  in  "Der  deutsche 
Verlag."  Compare  also  Ostwald's  article  on  Catalysis  in  Science  and 
the  Arts,  in  the  Zeitschrift  fur  Electrochemie,  7,  995,  1901. 


16  ELECTROCHEMISTRY. 

The  Gas  Laws.     Work  Obtainable  from  the  Expansion 
of  Gases. 

We  will  later  find  that  the  method  of  calculating  the 
work  obtainable  from  the  expansion  of  a  gas  is  also 
applicable  in  calculating  the  work  done  when  substances 
in  a  solution  change  their  concentration.  We  will  there- 
fore briefly  go  over  the  gas  laws  and  put  them  in  a  form 
from  which  the  work  obtainable  is  easily  calculated. 

1.  Boyle's  Law. — At  constant  temperature,  when  the 
volume  of  a  gas  is  changed,  the  pressure  varies  inversely 
as  the  volume;  that  is, 

p-v  =  B,  constant. 

If  we  bring  into  the  volume  of  i  litre  successively  one, 
two,  three, .  .  .  grams  of  oxygen,  the  pressure  increases  in 
the  proportion  one,  two,  three,  .  .  .  ;  i.e.,  each  gram  of 
oxygen  presses  on  the  walls  of  the  containing  vessel  as 
though  it  were  present  alone. 

2.  Gay-Lussac's  Law. — If  the  pressure  on  a  gas  is 
kept  constant  and  the  temperature  raised,  the  gas  expands 
per  degree  centigrade  by  an  amount  which  is  0.003663 
times  (  =  -2T-g-)  the  volume  it  occupies  at  o°  C.     If  the 
volume  at  o°  C.  is  v0,  its  volume  (v)  at  the  temperature 
r°  C.  is 

V  =  v0(i  +  0.003663  •  T). 

On  the  other  hand,  if  the  volume  is  kept  constant  during 
the  heating,  the  pressure  increases.  Boyle's  law  holds 
for  any  given  temperature,  and  it  therefore  follows  by 
combining  these  two  equations  that 

^  =  MI +0.0036637). 


WORK,   CURRENT    AND   VOLTAGE.  i? 

If  both  pressure  and  volume  vary,  we  obtain  for  the 
product  at  the  temperature  T°  C. 

p-V  =  pQ-V0(l  +0.0036631-). 

This  equation  holds  on  the  supposition  that  a  gas  exerts 
no  pressure  at  the  absolute  zero,  and  affords  a  means  of 
calculating  this  temperature.  The  value  thus  found  is 
—  273°  C.  If  T  represents  the  absolute  temperature 
(  =  273  +  T)  (cf.  p.  10)  we  obtain  the  equation 


^ 
pv  =  L  --  T. 

273 

3.  From  section  i  it  is  seen  that  each  gram  of  a  gas 
exerts  a  pressure  on  the  walls  of  the  containing  vessel  as 
though  it  were  present  alone.     This  applies  also  to  a 
mixture  of  two  or  more  different  gases,  and  the  pressure 
of  a  gas  mixture  is  therefore  equal  to  the  sum  of  the 
pressure  which   each  gas  would   exert  by  itself.     This 
single  pressure  of  each  gas  which  goes  to  make  up  the. 
total  is  called  the  partial  pressure  of  the  gas  in  question. 

ILLUSTRATION:  The  pressure  of  the  atmosphere  at 
sea-level  under  normal  conditions  is  760  mm.  of  mercury, 
and  this  is  made  up  of  the  partial  pressures  due  to  nitro- 
gen, oxygen,  carbon  dioxide,  water-vapor,  and  the  rare 
gases.  Air  contains  about  79.2%  nitrogen,  20.8% 
oxygen,  and  about  0.04%  carbon  dioxide.  The  partial 

pressure  of  nitrogen  is  therefore  760  —  -  mm.  of  mercury, 

20.8 

and  that  of  oxygen  760-  -  mm. 

4.  When  gases  combine  to  form  a  chemical  compound 
the  volumes  which  react  are  either  equal  or  stand  in  a 
simple  numerical  proportion   to   one  another,   and   the 


i8  ELECTROCHEMISTRY. 

same  is  true  of  the  resulting  product  if  it  remains  in  the 
gaseous  form.  These  facts  form  the  basis  of  Avogadro's 
Hypothesis  (1811),  which  states  that  under  the  same 
conditions  of  temperature  and  pressure  the  unit  volume 
of  alt  gases  contains  the  same  number  of  molecules* 

ILLUSTRATION:  2  grs.  of  hydrogen,  32  grs.  oxygen, 
44  grs.  carbon  dioxide,  28  grs.  nitrogen  always  occupy  the 
same  volume  when  the  temperature  and  pressure  of  each 
has  the  same  value.  At  atmospheric  pressure  and  o°  C. 
this  volume  is  22.42  litres.  Or  if  a  mol  of  any  gas  at  o°  C. 
is  confined  in  the  volume  of  i  litre,  it  exerts  a  pressure  of 
22.42  atmospheres  on  the  containing  walls.  The  equation 
of  section  2,  therefore,  when  applied  to  i  mol,  becomes 


litre  atmospheres. 

273          273 

This  factor  0.0821  which  is  the  same  for  all  gases  is  a 
very  important  one.  It  is  called  the  "gas  constant"  and 
is  denoted  by  the  letter  R.  If  we  consider  n  mols  instead 
of  one  the  equation  is  of  course 

pv  =  nRT. 

ILLUSTRATION:  The  average  volume  of  i  mol  of  the 
different  gases  at  o°  C.  and  i  atmosphere  pressure  has 
been  found  to  be  22.42  litres.  Atmospheric  nitrogen  gave 
a  somewhat  different  value,  22.34.  This  led  to  an 
investigation  into  the  purity  of  atmospheric  nitrogen  and 
resulted  in  the  discovery  of  argon  and  the  other  rare 
gases. 

*  A  mol  or  gram-molecule  is  that  number  of  grams  of  a  substance 
which  is  equal  to  the  molecular  weight,  i  mol  of  Zn=65-4  grs.  Zn. 
i  mol  (^2=35.45  +  35.45  grs.  =  70.9  grs.  chlorine,  i  mol  CuSO4= 
63.6  +  32X64  grs.  =  158.6  grs.  CuSO4,  etc, 


WORK,   CURRENT,   AND   VOLTAGE.  19 

To  calculate  the  work  obtainable  from  an  expanding 
gas  one  must  remember  that  work  =  pressure  X  change 
in  volume,  provided  during  the  process  the  pressure 
does  not  change.  If  the  volume  is  kept  constant  and  the 
pressure  changes,  the  work  is  =  volume  X  pressure  change. 

If  we  let  a  gas  under  constant  pressure  and  tempera- 
ture expand  from  the  volume  Vi  to  volume  v2  the  work 
obtained  is 

A=p(v2-vi). 

Or  if  a  quantity  of  gas  at  constant  temperature  and 
constant  volume  has  its  pressure  raised  from  pi  to  p2  then 

A=v(p2-pl). 

ILLUSTRATION  i.  Let  us  consider  a  cylinder  v;hose 
cross-section  is  one  square  decimetre  and  whose  height  is 
about  3  metres,  at  the  bottom  of  which  is  i  mpl  =  i8  grs. 
of  water.  Suppose  the  water  is  converted  into  vapor  at 
o°  and  under  the  atmospheric  pressure.  Neglecting  the 
volume  of  the  liquid  water  (0.018  litre)  and  remembering 
that  at  o°  and  atmospheric  pressure  i  mol  of  every  gas 
occupies  the  volume  of  22.42  litres,  we  find  that  the  weight 
of  the  atmosphere  above  the  cylinder  is  raised  through 
a  distance  of  22.42  decimetres.  Since  the  work  which  is 
necessary  to  overcome  the  pressure  of  i  atmosphere 
through  the  volume  of  i  litre  is  r  litre-atmosphere,  we 
find  the  work  on  evaporation 

A  =22. 42  litre-atmospheres. 

If  n  mols  are  evaporated  the  work  is  of  course  n- 22.42 
litre-atm.  =  n- 231. 60  kg.-metres,  or  542.34  calories 
(cf.  Table  5). 


20  ELECTROCHEMISTRY. 

ILLUSTRATION  2.  If  we  decompose  by  electrolysis 
i  gr. -molecule  of  water,  we  obtain  2  grs.  of  hydrogen  and 
1 6  grs.  of  oxygen  =  i  mol  hydrogen +  J  mol  oxygen; 
these  occupy  under  standard  conditions  33.63  litres, 
That  is,  in  order  to  liberate  the  gas  into  the  atmosphere 
we  have  done  33.63  litre- atmospheres  of  work,  aside  from 
the  chemical  work  necessary  to  decompose  the  water. 
This  consideration  frequently  enters  into  the  calculation 
of  the  work  necessary  in  such  reactions  where  a  gas  is 
evolved  or  absorbed.  If  we  let  the  hydrogen  and  oxygen 
again  combine,  the  volume  decreases  by  33.43  litres;  i.e., 
the  atmosphere  in  this  case  does  33.43  litre -atmospheres 
of  work,  which  we  can  obtain  as  electrical  work  by  using 
a  gas-battery. 

In  general  it  \i\\\  not  be  true  that  the  volume  alone  or 
the  pressure  alone  varies.  If  we  have  a  quantity  of  gas 
and  increase  its  volume  at  a  constant  temperature,  the 
pressure  falls  off  at  the  same  time  according  to  the  equa- 
tion pv  =  constant.  To  calculate  the  work  we  need 
the  help  of  differential  calculus,  and  find  the  following 
result:  When  a  mol  of  a  gas  expands  from  vi  to  ^2  the 
work  obtainable  is  * 

A=RTln-. 

Vi 

Osmotic  Pressure  and  Osmotic  Work. 

It  has  been  shown  by  van't  Hoff  that  the  gas  laws 
mentioned  above  also  apply  to  substances  in  dilute  solu- 
tions. 

*  Ln  is  the  symbol  of  the  "natural  logarithm."  To  change  it  to  the 
Briggs  or  common  logarithm  it  must  be  multiplied  by  0.4343.  The 
derivation  of  the  above  equation  is  here  given  for  the  benefit  of  those 


WORK,  CURRENT,  AND   VOLTAGE.  21 

The  pressure  of  a  gas  is  to  be  looked  upon  as  its  endeavor 
to  expand.  Gases  expand  as  far  as  they  can,  i.e.,  they 
distribute  themselves  through  the  whole  of  the  volume 
at  their  disposal  if  there  is  a  medium  present  through 
which  they  can  pass.  Such  a  medium  is  the  vacuum  or 
any  space  filled  with  other  gases.  When  their  expansion 
is  hindered  by  a  medium  through  which  they  cannot  pass, 
such  as  an  air-tight  wall,  they  exert  on  this  wall  a  pressure. 

All  other  substances  behave  in  this  respect  similar  to 
gases.  All  have  the  tendency  to  distribute  themselves 
as  much  as  possible,  but  can  only  do  so  in  a  suitable 
medium.  Water  is  a  suitable  medium  for  cane-sugar. 
Sugar  tries  to  distribute  itself  in  this  medium  to  the 
greatest  possible  degree,  i.e.,  it  dissolves  in  water.  If  a 
layer  of  pure  water  is  carefully  put  over  a  solution  of 

who  have  studied  calculus.  When  the  gas  expands  from  v  to  the  vol- 
ume v  +  dv,  the  pressure  decreases  from  p  to  p  —  dp;  the  work  obtained, 
dA  therefore  lies  between  pdv  and  (p  —  dp)dv.  In  comparison  with  p, 
dp  is  infinitely  small  and  can  therefore  be  neglected;  i.e., 

dA  =  pdv. 

If  we  insert  the  value  of  p  which  is  obtainable  from  p-v=RT  in  this 
equation  we  obtain 


v 
This,  integrated  between  the  values  i)\  and  v2,  gives 

A  =  RTln^. 

Vi 

Since  vz:v\=  p\:  p2,  the  equation  can  also  be  written 


P2 

If  n  mols  of  gas  are  used,  the  equation  is 


2  2  ELECTROCHEMIS7R  Y. 

sugar,  the  sugar  has  an  opportunity  for  further  expansion, 
and  it  accordingly  diffuses  upwards  against  the  force  of 
gravity  till  the  concentration  at  all  points  is  the  same. 
If  the  two  layers  are  separated  by  a  wall  which  is  permeable 
to  water  but  not  to  the  sugar  molecules,  the  process  is 
reversed,  the  sugar  no  longer  diffuses  upwards,  but 
draws  water  through  the  wall  to  itself.  If  the  vessel 
containing  the  solution  is  closed  on  all  sides,  very  little 
water  can  enter,  since  a  hydrostatic  pressure  is  soon 
developed  which  prevents  the  further  entrance  of  water. 
This  tendency  to  expand  has  therefore  the  nature  of  a 
pressure,  and  is  called  the  osmotic  pressure  of  the  sugar 
solution.  The  relation  between  osmotic  and  gas  pres- 
sure is  clear  when  we  remember  that  the  gas  corresponds 
to  the  dissolved  sugar  and  the  solvent  (water)  to  the 
vacuum. 

If  we  avoid  the  development  of  hydrostatic  pressure, 
by  allowing  the  containing  vessel  to  give  way,  the  solution 
actually  draws  in  a  great  quantity  of  water. 

To  test  this  conclusion  experimentally  we  require  a 
substance  which  is  permeable  to  water  but  impermeable 
to  the  dissolved  sugar  molecules.  A  diaphragm  built  of 
such  a  substance  is  called  "semi-permeable." 

We  will  first  go  over  the  history  of  our  knowledge  con- 
cerning osmotic  pressure  and  at  the  same  time  become 
acquainted  with  many  terms  and  laws  which  will  be 
met  later  on. 

It  is  well  known  that  plant  cells  which  have  become 
dry  and  need  water  can  take  up  water  when  they  are 
put  in  contact  with  it,  without  losing  any  of  the  cell 
contents.  The  walls  of  plant  cells  are  therefore  semi- 
permeable  membranes.  The  first  investigations  on  the 


WORK,   CURRENT,  AND   VOLTAGE.  23 

osmotic  pressure  of  the  solution  in  plant  cells  were  made 
'by  physiologists.  The  cells  were  placed  in  salt  solutions, 
and  it  was  found  that  salt  solutions  of  a  particular  con- 
centration were  in  equilibrium  with  the  cells,  i.e.,  the 
cells  neither  expanded  nor  contracted.  If  they  were  put 
in  a  more  dilute  solution,  they  took  up  water  and  expanded; 
put  in  a  more  concentrated  solution  they  gave  off  water 
and  became  smaller.  Solutions  which  were  in  equilibrium 
with  the  cells  were  called  "  iso tonic  "  or  "  isosmotic  " 
solutions.  It  was  discovered  that  solutions  of  similar 
salts  were  isotonic  when  they  had  the  same  molecular 
concentration;  *  for  instance,  normal  solution  of  KNO3, 
NaNOs,  KC1,  NaCl  are  approximately  isotonic. 


Cell  Wall  ,_  Protoplasmic  Sac 


Nucleus 


As  Fig.  i  shows,  the  cells  are  surrounded  by  a  cell  wall 
which  is  permeable  to  solutions  as  well  as  water ;  within 
this  is  the  protoplasmic  sac  which  is  permeable  to 
water  but  not  to  the  salts  dissolved  in  the  cell  solution. 
Th.e  cell  solution  is  called  the  "protoplast,"  and  the  proc- 
ess of  expansion  or  contraction  is  called  "plasmolysis.'' 
A  fact  was  further  discovered  which  was  later  explained 
by  the  theory  of  electrolytic  dissociation,  namely,  that 

*  Measured  in  mols  per  litre.     Cf.  remark  on  p.  18. 


ELECTROCHEMIS  TR  Y. 


dilute  solutions  of  the  above-mentioned  inorganic  salts 
have  an  osmotic  pressure  which  is  practically  twice  as 
great  as  solutions  containing  an  amount  of  organic  sub- 
stances— urea,  sugar,  etc. — equal  in  molecular  concentra- 
tion to  that  of  the  inorganic  salts.  It  should  be  mentioned 
here  that  the  osmotic  pressures  were  later  measured  in 
atmospheres  and  that  the  ordinary  plant  cells  which 
contain  dissolved  glucose,  malates  of  calcium  and  potas- 
sium, sodium  chloride,  etc.,  have  an  osmotic  pressure  of 
about  4  to  5  atmospheres.  Certain  cells  used  for  storage 
purposes  in  plants  such  as  the  sugar-beet  have  a  pressure 
of  15  to  20  atmospheres.  In  young  plants  the  pressure 
is  still  higher.  The  cells  of  bacteria  have  an  especially 
high  osmotic  pressure,  .  which 
fact  may  perhaps  explain  their 
great  physiological  action. 

Plant  cells  could  only  be  used 
in  making  comparative  measure- 
ments; in  order  to  measure  the 
pressure  directly  in  atmospheres, 
it  was  necessary  to  construct  an 
artificial  protoplasmic  sac,  i.e.,  a 
semi-perrneable  membrane.  A 
membrane  composed  of  copper 
ferrocyanide  is  impermeable  to 
sugar  and  most  salts,  but  readily 
permeable  to  H2O.  Traube 
made  such  a  membrane  -by 
FIG.  2.  putting  a  solution  of  K4Fe(CN),} 

in  a  carefully  cleaned  porous  cell 

and  placing  the  cell  in  a  dilute  solution  of  CuSO4-     The 
two  substances  diffuse  toward  each  other  in  the  cell  wall 


WORK,   CURRENT,  AND   VOLTAGE  25 

and  form,  on  meeting,  a  precipitate  of  Cu2Fe(CN)6, 
thus  making  a  durable  semi-permeable  wall.  Using  this 
cell,  measurements  were  made  as  follows  (cf .  Fig.  2).  A 
sugar  solution  was  put  in  the  cell;  the  open  end  was  closed 
by  a  rubber  cork,  through  which  passed  a  long  glass  tube, 
and  the  whole  was  placed  in  pure  wrater.  The  osmotic 
pressure  of  the  sugar  in  solution  causes  water  to  be 
drawn  in  through  the  walls  of  the  cell  till  the  hydro- 
static pressure  of  the  column  of  water  in  the  upright 
tube  is  as  great  as  this  drawing  force,  i.e.,  as  great  as 
the  osmotic  pressure  of  the  solution.  The  hydrostatic 
pressure  is  easily  calculated  from  the  specific  gravity  of 
the  solution  and  the  height  of  the  water  column  in 
the  tube. 

An  experiment  made  by  Ramsay  at  the  suggestion 
of  Arrhenius  affords  a  striking  comparison  of  osmotic 
pressure  with  the  action  of  gases.  He  made  an  air-tight 
cell  the  bottom  of  which  consisted  of  a  thin  sheet  of  Pt, 
attached  a  manometer,  filled  the  cell  with  nitrogen,  and 
placed  the  whole  in  an  atmosphere  of  hydrogen.  Plati- 
num is  impermeable  to  nitrogen  but  permeable  to  hydro- 
gen, consequently  hydrogen  is  drawn  into  the  cell  just  as 
H2O  is  drawn  through  the  copper  ferrocyanide  membrane, 
and  the  increase  of  pressure  can  be  read  off  on  the 
manometer. 

The  first  quantitative  osmotic  measurements  were  made 
by  the  physiologist  Pfeffer.  He  measured  the  osmotic 
pressure  of  sugar  solutions  of  various  concentrations  and 
obtained  the  following  table. 

Concentration    of    sugar    in 

grams  per  100  c.c i  2  2.74  4  6 

Pressure  in  atmospheres.  ...  0.704  i-34  i-97  2-7S  4.06 

Pressure  per  gram  of  sugar  .  0.704  0.67  0.72  0.69  0.68 


26 


ELECTROCHEMISTR  Y. 


From  these  figures  it  is  clear  that  the  pressure  is  pro- 
portional to  the  percentage  of  sugar  in  the  solution,  or 
inversely  proportional  to  the  volume  which  contains  a 

Constant 
gram  of  sugar  in  solution  p= ;   p  •  v  =  Constant, 

which  is  the  expression  of  Boyle's  law. 

Pfeffer  found  further  that  the  osmotic  pressure  rises 
with  a  rise  in  temperature,  as  the  following  table  shows. 


t 

Pressure 

Difference 

Observed 

Calculated 

6.8 

o 

664  atmosphere 

o  .  665  atmosphere 

+  0 

001 

13-7 

o 

691 

0.681 

—  o 

OIO 

14.2 

o 

671 

0.682 

+  0 

on 

15-5 

0 

684 

0.686 

+  0 

002 

22.  O 

o 

721 

o.  701 

—  o 

020 

32.0 

o 

716 

0.725 

+  0 

009 

36.0 

o 

746 

°-735 

—  o 

Oil 

The  calculated  pressures  in  the  third  column  were 
obtained  from  the  value  for  a  i%  solution,  according  to 
the  equation 

^=0.649(1+0.003671:)  atm.; 

for  an  n%  solution, 

p  =  n-  0.649(1  +0.003677). 

At  13.7°  C.  the  pressure  of  a  4%  solution  was  2.74 
atmospheres,  while  the  formula  gives  2.73.  If  we  calculate 
from  this  the  value  of  the  osmotic  pressure  for  i  gram- 
molecule  of  sugar  =  342  grs.  in  i  litre  we  obtain  the 
equation 

(Gay-Lussac's  law), 


WORK,    CURRENT,  4ND   VOLTAGE. 


27 


where  p  is  the  osmotic  pressure  in  atmospheres,  v  the 
volume  in  litres,  and  T  the  absolute  temperature.  Gay- 
Lussac's  law,  therefore,  holds  for  the  osmotic  pressure  of 
sugar ;  that  is,  the  sugar  exerts  the  same  osmotic  pressure 
as  it  would  exert  gaseous  pressure  if  the  H2O  were  absent 
and  the  sugar  in  the  form  of  a  gas. 

We  will  now  describe  a  few  experiments  which  strik- 
ingly illustrate  the  action  of  osmotic  pressure  and  at  the 
same  time  form  a  transition  to  considerations  on  the 
relation  between  osmotic  pressure  and  the  freezing-  or 
boiling-points  of  solutions. 

i.  When  a  crystal  of  Feds  .is  thrown  into  a  dilute 
solution  of  K4Fe(CN)6  a  membrane  of  Prussian  blue  is 
formed  on  the  outside  of  the  crystal.  Inside  this  mem- 
brane the  concentration  of  FeCls  is  very  high,  and  water 
is  drawn  in  from  the  outer  solution,  and  the  membrane  is 
extended  till  it  can  no  longer  stand  the  pressure  from 
within.  It  breaks  at  some  point  and  concentrated  solu- 
tion from  within  bursts  out.  A  fresh  membrane  is  at 
once  formed  around  this  and  the  process  is  repeated  so 
that  a  tree-like  structure  of  Prussian  blue  gradually  grows 
up  from  the  crystal. 


Solution 


Water 


FIG.  3. 

2.  If  a,  wall  of  ice  is  placed  in  a  rectangular  vessel 
(Fig.  3)  in  one  side  of  which  is  water  and  in  the  other 
a  solution,  the  ice  wall  will  appear  to  move  toward  the 


28  ELECTROCHEMISTRY. 

side  where  the  water  is,  because  on  the  one  side  ice  melts 
in  contact  with  the  solution,  while  water  crystallizes  out 
on  the  other  side.  This  ice  wall  is  in  a  way  a  semi- 
permeable  wall  which  is  permeable  to  water.  (An 
important  point  in  calculating  the  depression  of  the 
freezing-point.) 

3.  The  atmosphere  can  also  be  considered  as  a  semi- 
permeable  medium.     If  two  beakers,  one  of  which  con- 
tains a  sugar  solution  and  the  other  water,  are  placed  in 
a  confined  space,  it  will  be  found  that  water  distils  over 
from  the  second  to  the  first.     The  atmosphere  can  be 
considered  in  this  case  "as  a  wall  permeable  to  water  but 
not  to  sugar  molecules.     (Important  in  calculating  the 
elevation  of  the  boiling-point.) 

4.  The  so-called  "  Schlierenapparat  "  of  Tammann  is 
an  arrangement  for  observing  the  concentration  changes 
on  a  semi-permeable  wall.     If  a  drop  of  a  concentrated 
solution  of  K4FeCy6  is  carefully  brought  into  a  dilute 
solution  of  CuSO4  by  means  of  a  pipette,  a  membrane  of 
Cu2FeCy2  is  at  once  formed  around  the  drop.     Water 
will  be  drawn  in  through  the  membrane  on  account  of 
the  higher  osmotic  pressure  of  the  salt  inside,  and  as  a 
result  the  CuSCU  solution  in  the  immediate  vicinity  of 
the  drop  becomes  more  concentrated  and  this  heavier 
solution  can  be  seen  falling  in  a  stream  away  from  the 
drop.     If  no  descending  streams  are  observed,  the  two 
solutions  are  iso tonic.* 

We  have  seen  (p.   27)  that  the  gas  laws  hold  for  dilute 
solutions.      Just    as  gases   can  do  work  on  expanding, 

*  For  further  methods  of  measuring  osmotic  pressure,  as  well  as 
freezing-  and  boiling-point  changes,  see  any  of  the  larger  text-books  of 
physical  chemistry,  as  Nernst,  p.  132  ff. 


WORK,   CURRENT,  AND   YOLTAGE.  29 

k 

so  a  dilute  solution  can  be  made  to  perform  work  when  it 
is  being  further  diluted,  since  dilution  is  nothing  more 
than  the  distribution  of  the  dissolved  substance  through 
a  greater  volume,  i.e.,  expansion.  If  v  is  the  volume  in 
which  n  gram-  molecules  of  a  simple  substance,  for 
instance  cane-sugar,  are  dissolved,  and  if  the  osmotic 
pressure  of  these  molecules  is  lowered  by  dilution  from 
pi  to  p2,  the  work  which  may  be  obtained  is  (cf.  p.  20) 


or,  since  osmotic  pressure  and  concentration  are  directly 
proportional, 

A=nRTln-, 
c2 

or,  finally,  since  the  osmotic  pressure  varies  inversely  as 
the  dilution, 

(  Dilution  =  volume  per  gram-molecule  =  —  —  -.  —  I  • 

\  concentration/ 

Vo 

A=nRTln-. 

Vi 

With  the  help  of  this  equation  it  is  possible  in  most  cases 
to  calculate  the  work  obtainable  from  chemical  reactions. 


Calculation  of  Chemical  Work  from  Osmotic  Pressure. 
van't  Hoff's  Equation. 

We  will  take  a  reaction  of  the  form 


i.e.,  a  reaction   in  which   m  mols  of  the  substance  A 
unite  with  n  mols  of  thesubstance  B,  forming  o  mols 


3° 


ELEC  TROCHE  MIS  TR  Y. 


of  the  substance  C  and  q  mols  of  D.  For  instance  in  the 
reaction 

4SbCl3  +  5H2O  =  Sb4O5Cl2  +  loHCl, 

m  =  4,  n=  5,  0  =  1,  and  q=  10.  Further,  let  the  small  italic 
and  Greek  letters  represent  the  concentrations  before 
and  after  the  reaction  and  we  have  the  following  scheme : 


Disappearing 
Substances. 

Resulting 
Substances. 

A. 

B. 

C. 

D. 

Concentration  before  reaction.  .  . 
Concentration  after  reaction  
Number  of  reacting  molecules.  .  .  . 

a 
a 
m 

b 

f 

n 

C 

r 

0 

d 

9 

1 

As  the  reaction  goes  on,  the  concentration  of  both 
A  and  B  sinks.  Lowering  of  a  concentration  or  pres- 
sure can  do  work.  For  the  substance  A  this  work  is 


for  B  it  is 


mRTln-, 
a 


The  concentrations  of  C  and  D  are  increased  by  the 
progress  of  the  reaction.  The  work  to  be  gained  from 
this  cause  is  negative,  i.e.,  to  increase  their  concentration 
requires  work;  consequently 


-oRTln-=oRTln-> 

f  C 

7 


WORK,   CURRENT,  AND   YOLTAGE.  31 

The  total  work  of  the  reaction  is  therefore 


This  is  the  so-called  "  energy  equation  "  of  van't  HofL 
This  equation  becomes  still  simpler  when  we  introduce 
the  laws  of  mass  action.  When  the  reaction  goes  to 
completion,  i.e.,  till  equilibrium  between  all  the  reacting 

r°dq 
substances  prevails  (cf.  following  chapter),  and  #  =  -—  ^ 

represents  the  equilibrium  constant,  then 

Product  of  active  masses*  of  disaDpeariie:  substances 
A  =  RTlnK+RTln     Product  of  active  masses  Of  resulting  substances    ' 

When  all  the  substances  have  the  same  concentration 
at  the  start,  then 

A=RTlnK. 


*  In  this  equation  by  "active  mass"  of  a  substance  is  meant  the  con- 
centration of  the  same  raised  to  a  power  represented  by  the  number  of 
molecules  with  which  it  enters  into  the  reaction. 


CHAPTER  II. 

CHEMICAL  EQUILIBRIUM,   STATICS,   AND   KINETICS. 

THE  first  equation  on  page  31  gives  the  work  of  a 
reaction  when  it  is  interrupted  at  a  particular  point  where 
the  concentrations  are  a,  /?,  7-,  d.  We  will  now  consider 
the  far  more  important  question,  how  much  work  a 
reaction  can  afford  when  we  let  it  go  on  till  it  stops  of 
itself.  We  have  a  fundamental  distinction  to  make 
between  the  so-called  complete  and  incomplete  reactions. 

An  example  of  a  complete  reaction  is  the  conversion 
of  water  into  steam  at  atmospheric  pressure  and  tem- 
peratures above  100°,  when  the  water  " phase"  completely 
disappears. 

The  freezing  of  water  below  o°  is  likewise  a  complete 
reaction.  Water  is  turned  completely  into  ice,  there  is 
no  unfrozen  remainder. 

The  evaporation  of  water  at  temperatures  below 
1 00°  and  at  atmospheric  pressure  is  an  example  of  an 
incomplete  reaction.  In  this  case  water  will  evaporate 
till  the  partial  pressure  (cf.  p.  17)  of  the  water-vapor 
attains  a  value  which  is  just  the  same  as  the  vapor  pres- 
sure of  water  at  the  temperature  which  prevails.  When 
such  a  concentration  of  the  water-vapor  is  attained 
just  as  much  water  evaporates  as  is  formed  by  condensa 

32 


CHEMICAL   EQUILIBRIUM,  STATICS,  AND  KINETICS.      33 

tion  of  the  vapor,  i.e.,  visible  evaporation  has  stopped. 
We  say  the  liquid  water  is  in  equilibrium  with  water- 
vapor  at  the  corresponding  vapor  pressure.  If  too  little 
water  is  present,  it  will  of  course  evaporate  completely. 

A  classical  example  of  an  incomplete  reaction  is  the 
"  ester  formation."  When  one  mol  each  of  alcohol 
and  acetic  acid  are  brought  together  they  unite  to  form 
ethyl  acetate  and  water,  but  the  reaction  is  not  complete; 
it  stops  when  f  mol  of  ester  and  §  mol  of  water  have 
been  formed  and  J  mol  of  alcohol  and  J  mol  of  acid 
remain  unaltered.  The  reaction  has  reached  equilibrium 
when  the  concentrations  have  attained  these  values. 

We  will  have  to  do  principally  with  the  incomplete 
reactions.  It  was  formerly  thought  that  such  reactions 
were  exceptional,  because  the  end  concentrations  were 
too  small  to  be  measured  chemically.  For  instance,  before 
Davy's  time  certain  substances  were  considered  absolutely 
insoluble.  It  was  believed  that  when  solutions  of  barium 
chloride  and  sulphuric  acid  were  mixed,  barium  sulphate 
was  absolutely  removed  from  the  solution.  According 
to  this  idea  such  a  reaction  would  be  complete.  In 
reality  there  is  no  such  thing  as  an  absolutely  insoluble 
substance,  although  in  many  cases  the  solubility  is  so 
small  that  chemical  methods  are  unable  to  measure  it. 
The  precipitation  of  substances  is  in  reality  an  incomplete 
reaction.  It  was  formerly  thought  that  when  zinc  in 
excess  was  put  in  a  solution  of  copper  sulphate  absolutely 
all  the  copper  was  precipitated  out  of  the  solution.  But 
this  is  not  the  case,  the  reaction  goes  on  till  the  concen- 
tration of  the  copper  salt  is  io~40.  Of  course  it  is  out  of 
the  question  to  even  demonstrate  by  chemical  means  the 
presence  of  copper  in  such  a  dilute  solution,  but  certain 


34  ELECTROCHEMISTRY. 

electrochemical  methods  enable  us  to  approximately 
measure  such  low  concentrations.  All  such  reactions 
in  which  one  metal  is  precipitated  by  another  are  in- 
complete. They  are  also  reversible.  We  saw  above 
that  alcohol  and  acetic  acid  unite  to  form  ethyl  acetate 
and  water.  When  we  dissolve  a  mol  of  ethyl  acetate 
in  i  mol  of  water  the  reverse  reaction  occurs,  i.e.,  alcohol 
and  acetic  acid  are  formed.  But  this  reaction  is  also 
incomplete,  and  will  come  to  the  same  state  of  equilibrium 
as  the  first,  i.e.,  will  stop  when  J  mol  of  ethyl  acetate 
has  been  converted  into  acid  and  alcohol. 

Such  reactions  which  can  occur  in  either  direction  are 
denoted  by  two  arrows  in  place  of  the  equality  sign: 

C2H5OH  +  CH3COOH  <=>  CH3COOC2H5  +  H2O. 

We  have  defined  an  incomplete  reaction  as  one  which 
ceases  of  itself  when  equilibrium  is  reached.  This 
definition  requires  some  modification:  when  equilibrium 
is  reached  the  reaction  does  not  actually  cease,  but  the 
two  reactions,  from  left  to  right  and  the  reverse,  both  go 
on  with  the  same  velocity,  so  that  although  a  continual 
reaction  is  going  on  the  composition  of  the  equilibrium 
mixture  remains  constant.  We  must  likewise  assume 
a  similar  condition  of  affairs  before  equilibrium  is  reached. 
Both  reactions  take  place,  but  the  velocity  in  one  direction 
is  much  greater  than  in  the  other,  so  that  this  determines 
the  direction  of  the  total  reaction  which  we  observe. 

Keeping  in  mind  these  considerations  we  will  have 
little  difficulty  in  understanding  the  very  important 
law  of  mass  action. 

Let  us  take  the  reaction  of  page  29, 


CHEMICAL  EQUILIBRIUM,   STATICS,  AND  KINETICS.     35 


in  which  the  concentrations  of  A  ,  B,  C,  D  are  represented 
by  a,  b,  c,  d  respectively.  The  kinetic  theory  *  and  also 
practical  experience  teach  that  the  reaction  from  left  to 
right  can  be  expressed  by  the  equation 

•vi  =  kiambn, 

i.e.,  is  proportional  to  the  product  of  the  active  masses 
of  the  reacting  substances.  In  the  same  way  the  velocity 
of  the  reverse  reaction  can  be  expressed: 


But  the  actual  apparent  velocity  is  the  difference  between 
these  two  single  velocities: 

V=V!-v2  =  kiambn  -  k2c°dq. 

This  is  the  law  of  chemical  kinetics. 

When  equilibrium  is  attained  Vi  =  v2  and  the  total 
velocity  V  becomes  o.  Consequently  when  the  equilibrium 
concentrations  are  a? 


If   j-  =  K   represents   the   equilibrium   constant   of   the 
#1  , 

reaction,  then 


*  The  kinetic  theory  assumes  that  the  molecules  of  all  substances 
are  in  a  continual  state  of  motion;  a  reaction  can  only  occur  when  two 
or  more  molecules  collide.  See  Nernst,  Theoretische  Chemie,  1903, 
p.  427. 


( 


36  ELECTROCHEM1S  TR  Y. 

This  is  the  law  of  chemical  statics.  It  states  that  for  every 
incomplete  reaction  there  exists  a  state  of  equilibrium 
when  the  reaction  ceases  of  itself,  and  this  condition  is 
regulated ,  by  the  active  masses  *  of  the  disappearing 
substances  and  of  those  being  produced.  The  equilibrium 
constant  remains  the  same  no  matter  what  the  concentra- 
tions of  the  reacting  substances  were  at  the  start.  For 
instance,  in  the  reaction 

CH3COOH  +  C2H5OH  <=>  CH3COOC2H5+H2O 

*  We  must  explain  the  conception  of  "active  mass"  somewhat  more 
definitely.  By  the  active  mass  of  a  substance  is  meant  its  volume  con- 
centration; in  the  case  of  a  solution  it  is  the  ordinary  molecular  concen- 
tration (gr.-mols  per  litre).  In  the  formulae  of  the  law  of  mass  action, 
the  energy  equation,  etc.,  the  active  mass  of  each  molecule  which  takes 
part  in  the  reaction  is  used;  the  concentration  a  of  the  substance  A, 
for  instance,  appears  m  times  since  m  molecules  of  A  take  part  in  the 
reaction. 

If  a  solvent  takes  part  in  a  reaction,  as  for  instance  water  in  the 
ester  formation  or  in  hydrolysis,  its  active  mass  should  also  be  intro- 
duced. In  dilute  solutions,  however,  the  change  in  the  active  mass  of 
water  is  so  slight  that  for  practical  purposes  it  may  be  neglected,  and 
its  active  mass  be  considered  as  a  constant  (in  all  such  calculations  the 
change  in  active  mass  is  the  important  point  rather  than  the  absolute 
value  itself).  In  very  concentrated  solutions  the  change  in  active  mass 
of  the  solvent  can  no  longer  be  neglected,  but  in  most  of  the  electro- 
chemical reactions  of  importance,  concentrated  solutions  play  a  minor 
part,  and  we  may  nearly  always  consider  the  active  mass  of  the  solvent 
as  constant. 

The  active  mass  of  a  solid  in  contact  with  a  solution  in  which  the 
solid  reacts  is  constant. 

The  active  mass  of  a  metal  in  a  galvanic  cell,  or  of  a  soluble  sub- 
stance in  excess  in  a  solution  saturated  with  respect  to  this  substance, 
is  constant,  for  as  soon  as  any  more  of  the  substance  is  formed  or  used 
up  the  concentration  of  saturation  is  at  once  reproduced  by  further 
precipitation  or  solution  of  the  solid,  and  the  active  mass  remains  un- 
changed. 


CHEMICAL  EQUILIBRIUM,  STATICS,  AND  KINETICS.    37 

if  we  start  with  i  gr.-mol  each  of  acid  and  alcohol, 
equilibrium  is  reached  when  J  mol  of  acid  and  alcohol  is 
left  and  §  mol  of  ester  and  water  are  formed.  K  is 
therefore 

K 

" 


If  instead  of  taking  one  mol  each,  to  start  with,  we 
take  any  concentration  we  please,  the  reaction  will  go 
on  in  any  case  till  the  ratio  of  the  concentrations  is  J. 
For  instance,  if  we  take  2  rnols  of  acid  to  i  of  alcohol, 
there  will  of  course  be  more  than  J  mol  of  acid  left  over. 
If  x  represents  the  amount  of  acid  and  alcohol  which 
has  been  used  up  when  equilibrium  is  reached  the 
quantity  of  ester  and  water  formed  is  also  x. 

In  equilibrium,  then,  we  have  2—00  mols  acetic  acid, 
i—  x  mol  alcohol,  and  x  mol  each  of  ester  and  water, 

then  —    —^  --  =  K=—.    From  this  quadratic  equation 
x  4 

we  can  calculate  x,  and  then  know  how  far  the  reaction 
has  gone. 

Another  classical  example  is  the  formation  of  hydriodic 
acid  from  iodine  vapor  and  hydrogen,  according  to  the 
reaction  H^-I-^^^HL  Here  we  can*  use  instead  of 
the  concentration  the  partial  pressures  of  each  gas,  which 
are  directly  proportional  to  the  concentration.  If  P 
with  the  corresponding  indices  represents  each  particular 
partial  pressure,  then 


'HI 


ELECTROCHEMISTR  Y. 
A  further  example  is  the  reaction 


and 


Ppci5 


The  last  two  equations  have  to  do  with  the  breaking  up 
or  "  dissociation "  of  gases.  All  cases  of  dissociation 
equilibrium  whether  in  gases  or  in  solution  are  calculated 
in  a  similar  way. 

A  very  important  example  is  the  dissociation  of  carbon 
dioxide.  The  union  of  carbon  monoxide  with  oxygen  is 
an  incomplete  reaction;  thus,  2CO2<=±O2  +  2CO,  and  the 
equilibrium  conditions  are  given  by  K  X  Pi2  =  P%  X  Pa2, 
where  PI,  P'2,  PS  are  the  partial  pressures  of  the  three  gases 
respectively.  If  the  constant  K  has  been  determined 
at  some  particular  temperature  and  pressure,  the  dis- 
sociation can  be  calculated  by  the  above  equation  for 
any  pressure  at  this  particular  temperature.  The  follow- 
ing table  gives  the  percent  to  which  carbon  dioxide  is 
dissociated  into  carbon  monoxide  and  oxygen  not  only 
for  different  pressures  but  also  for  temperatures  between 
1000°  and  4000°. 


Pressures  in  Atmospheres 


O.OOI 

O.OI 

O.I 

i 

10 

100 

1000 

0.7 

o-3 

0.13 

0.06 

0.03 

0.015 

1500 

7 

3-5 

!-7 

0.8 

0.4 

0.2 

2000 

40 

12.5 

8 

4 

3 

2-5 

2500 

81 

60 

40 

T9 

9 

4.0 

3000 

94 

80 

60 

40 

21 

10 

35  °° 

96 

85 

70 

53 

32 

15 

4000 

97 

90 

80 

63 

45 

25 

CHEMICAL   EQUILIBRIUM,  STATICS,  AND  KINETICS.     39 

The  table  shows  that  at  high  temperatures  it  is  im- 
possible to  burn  carbon  monoxide  completely  to  the 
dioxide,  and  that  for  this  reason  we  are  unable  to  utilize 
at  high  temperatures  the  full  energy  of  the  combustion 
of  carbon;  we  can  see  from  the  table  about  how  far  the 
combustion  goes  in  different  processes. 

In  the  iron  blast-furnace  the  temperature  is  about 
2000°  and  the  partial  pressure  of  carbon  dioxide  is  about 
0.2  of  an  atmosphere.  Under  these  conditions  CO2  is 
about  5%  dissociated,  and  as  a  result  the  efficiency  of  the 
furnace  is  slightly  impaired.  In  illuminating  flames  which 
also  have  a  temperature  of  2000°  or  more,  the  partial 
pressure  of  CO 2  is  only  about  o.i  of  an  atmosphere  owing 
to  the  large  quantity  of  hydrogen.  The  dissociation  of 
CO2  can  then  exceed  10%,  and  the  temperature  is  cor- 
respondingly lower,  while  the  illuminating  power,  which 
varies  enormously  with  the  temperature,  is  very  appreci- 
ably decreased.  In  the  case  of  explosives  the  temperature 
is  probably  between  2500°  and  3000°,  but  here  the  pres- 
sure of  CO2  is  several  thousand  atmospheres,  and  the 
dissociation  very  small,  so  that  the  combustion  is  prac- 
tically perfect. 

The  law  of  mass  action  has  been  found  to  hold  for  a 
great  number  of  reactions ;  for  further  details,  reference  is 
made  to  the  text-books  of  theoretical  and  physical  chem- 
istry by  Nernst,  Ostwald,  and  others.  As  yet  we  have 
only  considered  reactions  between  substances  which  were 
in  the  same  physical  condition,  i.e.,  in  "  homogeneous 
systems  "  when  all  were  either  liquid  or  gaseous.  We  will 
now  consider  the  "  heterogeneous  "  systems. 

For  the  first  illustration  we  will  take  the  solution  of  a 
salt.  If  we  bring  solid  salt  in  contact  with  water  it  dissolves: 


40  ELECTROCHEMISTRY. 

NaClsolid  <=±  NaCldissolved. 

The  equilibrium  equation  is  ^•Cs'olid  =  Cdissolved;  but  the 
solid  salt  does  not  change  its  concentration  Csolid  as  solu- 
tion goes  on  ;  its  quantity  may  diminish  but  the  remaining 
solid  salt  always  keeps  the  same  density  or  concentration. 
Csolid  is  therefore  also  a  constant,  and  for  equilibrium 
we  have  KI  =  Cdissoived.  This  equation,  however,  is 
nothing  less  than  a  statement  that  at  equilibrium  the 
concentration  of  the  dissolved  salt  is  constant,  i.e.,  every 
salt  has  a  constant  solubility.  What  has  been  said  for 
ordinary  salt  is  true  for  all  solid  substances.  They  do 
not  change  their  concentration  as  solids  although  they 
may  lose  in  weight.  This  fact  is  expressed  when  we  say 
the  active  mass  of  a  solid  substance  is  constant  (cf  .  note, 

p.  36). 

2.  Another  classical  example  is  the  dissociation  of 
calcium  carbonate  :  CaCO3solid  <=±  CaOsolid  +  CO2gaSeous. 
Here,  too,  we  can  include  the  active  mass  of  the  solid 
substances  in  the  constant  of  equilibrium  and  obtain 


where  pco2  is  the  pressure  of  the  carbon  dioxide,  and  is 
proportional  to  its  concentration.  This  is  simply  a 
statement  that  the  dissociation  pressure  of  marble,  i.e., 
the  pressure  with  which  it  evolves  CO  2,  is  a  constant  at 
constant  temperature.  The  same  remarks  apply  also 
to  liquids.  When  liquid  water  evaporates,  part  of  it 
disappears  as  such,  but  the  density  of  the'  remaining 
water,  i.e.,  its  concentration  (mols  per  litre),  is  not 
changed.  We  obtain  in  this  case  also 


CHEMICAL  EQUILIBRIUM,  STATICS,  AND  KINETICS.     41 

in  other  words,  the  vapor  pressure  of  water  has  at  con- 
stant temperature  a  fixed  value. 

Change  of  Equilibrium  with  the  Temperature. 

In  the  previous  considerations  it  has  been  understood 
that  the  temperature  remains  constant.  If  we  consider 
a  reaction  at  different  temperatures,  as  for  instance 
the  formation  of  carbon  dioxide  (cf.  table,  p.  38),  we 


1000 


2000 J 
Temperature 

FIG.  4. 


3000 J 


4000 J 


find  that  the  equilibrium  constants  are  different  for 
each  temperature.  These  facts  are  clearly  shown 
by  the  accompanying  curves  (Fig.  4).  The  abscissae 
represent  temperatures,  and  the  ordinates  give  the  per- 
centage to  which  carbon  dioxide  is  dissociated.  At  low 
temperatures  the  combustion  for  all  practical  purposes 
is  complete,  and  the  gas  mixture  contains  practically 
100%  CO 2-  But  the  higher  the  temperature,  the  less 
complete  is  the  combustion.  At  a  temperature  of  3000° 
when  the  pressure  of  CO2  is  one  atmosphere  the  com- 


42  ELECTROCHEMISTRY. 

bustion  is  only  60%  of  the  whole;  the  dissociation 
increases  with  increasing  temperature,  till  finally  at  very 
high  temperatures  carbon  monoxide  and  oxygen  combine 
to  a  very  slight  extent.  However,  since  this  reaction,  either 
at  high  or  low  temperature,  is  not  absolutely  complete, 
the  curve  which  represents  the  relation  between  degree 
of  combination  and  temperature  can  never  actually 
touch  the  two  horizontal  lines  representing  o%  and  100% 
dissociation,  but  can  only  approach  them  asymptotically. 
This  is  best  seen  in  the  curve  for  o.ooi  of  an  atmosphere. 
The  relations  which  hold  for  this  particular  reaction  are 
true  for  all  incomplete  reactions;  similar  curves  can  be 
obtained  in  all  cases. 

From  what  has  been  said  it  can  be  seen  that  the  chem- 
ical facts  with  which  we  are  acquainted  are  somewhat 
a  matter  of  chance,  since  they  are  governed  by  the  tem- 
perature and  pressure  which  happen  to  prevail  on  our 
planet.  We  are  accustomed  to  say  that  coal  burns, 
uniting  with  oxygen  to  form  carbon  dioxide,  and  this 
is  true  for  the  comparatively  low  temperatures  of  our 
stoves  or  blast-furnaces.  But  if  we  lived  on  a  body 
whose  temperature  like  that  of  the  sun  is  in  the  neighbor- 
hood of  10000°  our  chemical  text-books  would  say  that 
carbon  and  oxygen  do  not  combine.  Carbon  dioxide 
would  be  an  unknown  substance  to  an  inhabitant  of  the 
sun,  since  at  that  temperature  it  is  almost  completely 
dissociated.  Water  is  an  unknown  body  on  the  sun,  since 
the  equilibrium  of  the  reaction  2H2  +  O2^2H2O  at  the 
sun's  temperature  lies  at  a  point  where  the  concentration 
of  the  water  is  immeasurably  small.  We  consider  a 
mixture  of  hydrogen  and  oxygen  unstable,  but  an  in- 
habitant of  the  sun  would  consider  water  an  exceedingly 


CHEMICAL   EQUILIBRIUM,  STATICS,  AND  KINETICS.     43 

unstable  compound  if  he  could  ever  succeed  in  obtain- 
ing it. 

Our  experimental  chemistry  is  the  chemistry  of  the 
earth;  we  cannot  write  a  "  chemistry  of  the  universe" 
until  we  know  the  equilibrium  constants  of  all  reactions 
at  all  temperatures.  For  since  all  reactions  proceed 
toward  the  point  of  equilibrium  we  could  then  know  the 
direction  in  which  any  reaction  would  go  at  any  tempera- 
ture. 

We  are  indebted  to  J.  H.  van't  HofT,  the  master  of  the 
science  of  physical  chemistry,  for  the  method  of  solving 
this  important  problem.  An  expression  derived  by  him 
and  known  as  "  van't  HofF s  Equation  "  gives  the  relation 
between  the  equilibrium  constant,  the  heat  of  reaction, 
and  the  temperature.  This  expression,  obtained  by  inte- 
grating a  differential  equation,*  is: 


In  this  equation  T\  and  T2  are  two  absolute  temperatures, 
KI  and  K2  the  equilibrium  constants  of  the  given  reaction 
at  these  temperatures,  In  represents  the  "  natural  log  " 
(see  p.  20,  note),  R  is  the  gas  constant  1.991  cal.  (see 
table  on  p.  5),  and  q  is  the  "  heat  of  reaction "  (see 
p.  8).  If  we  know  the  last-named  value  and  determine 
the  equilibrium  constant  for  any  particular  temperature 
we  can  calculate  the  equilibrium  for  any  other  tempera- 
ture. The  table  on  page  38  has  been  calculated  in  this 

*  The  equation  is  derived  from  the  second  law  of  thermodynamics 
(p.   9)   and  the  energy  equation  (p.  31).     By  combining  them  the  differ- 

dlnK      -q 
ential  equation  -rr^  ~7^,  1S  obtained. 


44  ELECTROCHEMISTR  Y. 

way,  sLice  it  is  experimentally  impracticable  to  measure 
the  equilibrium  at  a  temperature  of  4000°. 

On  the  other  hand,  if  we  know  the  equilibrium  constant 
of  a  reaction  at  two  different  temperatures  we  can  calculate 
the  "  heat  of  reaction."  The  equilibrium  constant  of 
the  reaction  where  a-  solid  substance  dissolves  in  water 
is  equal  to  the  concentration  at  saturation  (see  p.  40). 
If  Ci=2.SS  and  £2  =  4. 22  are  the  solubilities  of  succinic 
acid  at  o°  C.  (  =  273)  and  8.5°  C.  (  =  281.5),  then 

q  (  i         i  \ 
Inci  —  Inc2  = — (  7^ —  777-  ) . 

2\li       lz/ 

From  this  equation  we  can  calculate  q\  and  find  the 
value  —6900  cal.  The  reaction  mixture  cools  itself  off, 
since  q  is  negative.  Berthelot  found  experimentally 
—  6700  cal.  as  the  heat  of  solution,  in  very  good  agreement 
with  the  calculated  value. 


CHAPTER  III. 

THEORY  OF  ELECTROLYTIC  DISSOCIATION. 

A  NUMBER  of  experimental  facts  which  we  will  mention 
later  on  has  led  to  the  supposition  that  in  the  water 
solution  of  a  salt  only  a  certain  fraction  of  the  salt  plays 
a  part  in  electrochemical  processes.  This  active  part 
varies  with  the  nature  of  the  salt,  the  temperature,  the 
dilution,  and  the  nature  of  the  solvent.  (Solutions  in 
solvents  other  than  water  have  not  as  yet  been  system- 
atically investigated.)  The  rest  of  the  salt  remains  in- 
active and  has  nothing  to  do  in  transporting  the  electric 
current.  For  instance,  if  we  measure  the  conductivity  of  a 
sodium-chloride  solution,  we  find  that  all  the  salt  does  not 
take  part  in  conducting  the  current,  but  only  a  fraction; 
in  the  case  of  a  normal  solution  of  NaCl  this  active  part 
is  §  of  the  whole;  in  a  normal  solution  of  AgNO3  it  is  only 
58%.  It  is  this  same  fraction  which  is  active  in  in- 
fluencing the  electromotive  force  of  an  electrode;  for 
instance,  in  a  normal  AgNO3  solution  it  is  58%  of  the 
total  salt  present.  Of  every  .TOO  molecules  in  the  above 
NaCl  solution  67  are  in  a  condition  different  from  the 
remaining  33,  and  the  same  is  true  of  the  58  molecules  in 
every  100  in  the  AgNO3  solution.  This  active  part  of  the 
whole  is  found  from  the  conductivity  and  measurement 

45 


46  ELECTROCHEMISTRY. 

of  electromotive  forces,  and  also  from  measurements  of 
the  osmotic  pressure  and  changes  in  the  freezing-  and 
boiling-points  of  the  solutions,  and  all  these  methods 
give  practically  the  same  values. 

The  chemical  conduct  of  dissolved  salts  seems  to 
indicate  that  these  67  or  58  molecules  are  just  the  ones 
which  enter  into  chemical  reactions.  In  cases  where  no 
molecules  are  present  which  can  transport,  the  current,  or 
if  they  are  present  in  very  small  amounts,  chemical 
reactions  do  not  take  place,  or  if  they  do,  are  extremely 
slow.  A  salt  on  dissolving  in  water  must  therefore 
suffer  some  change,  and  the  physical  conduct  of  solutions 
shows  that  the  change  is  very  profound. 

Like  all  soluble  substances,  a  dissolved  salt  depresses 
the  freezing-point  of  water  and  raises  the  boiling-point. 
When  i  gr.-mol  of  a  substance  like  urea,  or  boric  acid, 
or  sugar,  which  does  not  conduct  the  current,  is  dissolved 
in  i  litre  of  water,  the  freezing-point  of  the  solution  is 
—  1.86°.  1.86  is  called  the  "molecular  lowering  of  the 
freezing-point  "  of  water.  If,  however,  we  take  a  solution 
of  i  gr.-mol  of  a  salt  in  i  litre,  which  does  conduct  the 
current,  we  find  that  the  freezing-point  is  lowered  more 
than  1.86°.  It  seems  as  though  that  part  of  the  salt 
which  does  not  take  part  in  the  conductivity  acts  normally 
in  lowering  the  freezing-point,  but  the  rest  which  is  the 
active  agent  in  conducting  the  current  acts  as  though  its 
component  radicals  had  parted  company  and  were  each 
existing  separately  in  the  solution.  For  instance,  in  a 
normal  solution  of  NaCl,  33%  of  the  salt  affects  the 
freezing-point  as  cane-sugar  would,  lowering  it  1.86X0.33 
=  0.614°;  but  the  remaining  67%  acts  as  though  it  had 
broken  up  into  Na  and  Cl  atoms  and  thus  affects  the 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.          47 

freezing-point  twice  as  much  as  an  equal  molecular 
quantity  of  sugar  would  do,  so  that  the  lowering  from 
this  cause  is  2  X  67  X  1.86  =  2.49.  The  total  lowering  is 
therefore  2.49  +  0.614  =  3.104°  instead  of  1.86°.  In  a 
normal  AgNOs  solution  42%  has  the  usual  effect,  but  the 
rest  has  twice  the  normal  effect,  as  if  this  part  of  the 
AgNO3  had  broken  up  into  Ag  and  NO3  radicals.  In  a 

N 
-  solution  of  H2SO4  about  75%  of  the  acid  takes  part  in 

conduction.  The  remaining  25%  acts  as  usual  in  de- 
pressing the  freezing-point,  but  the  75%  has  triple  the 
usual  effect,  as  though  it  had  broken  up  into  H+H  +  SO4. 
The  o.i  normal  acid  acts  therefore  in  regard  to  its  con- 
ductivity as  though  it  were  0.075  normal,  but  with  respect 
to  its  freezing-point  as  if  it  were  0.25  normal. 

The  relations  which  hold  for  the  lowering  of  the  freez- 
ing-point are  true  also  of  the  rise  of  the  boiling-point  or 
lowering  of  the  vapor  pressure.  A  gram-molecule  of  any 
non-conducting  substance  when  dissolved  in  i  litre  of 
water  raises  the  boiling-point  a  certain  fixed  amount,  no 
matter  what  the  substance  is,  provided  only  that  it  gives 
a  non-conducting  solution.  But  a  o.i  normal  solution 
of  H2SO4  raises  the  boiling-point  as  though  75%  of  the 
acid  had  decomposed  with  the  formation  of  three  new 
substances,  i.e.,  as  though  the  solution  Were  0.25  normal. 

The  osmotic  pressure  is  affected  in  just  the  same  way. 
On  p.  26  we  saw  that  a  normal  solution  of  cane-sugar 
exerted  an  osmotic  pressure  of  22.42  atmospheres.  A 
nopnal  solution  of  other  non-conducting  substances  has 
the  same  value,  but  a  conducting  salt  solution  has  a  much 
higher  osmotic  pressure.  The  ratio  of  this  higher  pres- 
sure to  22.42  is  the  same  as  the  ratio  of  the  abnormal 


48  ELECTROCHEMISTRY. 

to  the  normal  lowering  of  the  freezing-point.  Here  again 
the  conducting  molecules  act  as  though  they  had  broken 
up  into  their  component  radicals. 

These  facts,  as  well  as  many  others  of  a  physical  and 
chemical  nature,  leave  little  room  for  doubt  that  a  de- 
composition or  "  electrolytic  dissociation  "  actually  takes 
place  when  a  salt  is  dissolved  in  water,  and  that  only  the 
dissociated  atoms  or  molecules  (known  as  "  ions  ")  are 
the  active  agents  in  conducting  the  electric  current  or 
determining  the  electromotive  force  of  an  electrode.  The 
percentage  of  the  salt  which  undergoes  decomposition  is 
called  the  "  degree  of  dissociation." 

Aside  from  the  fact  that  many  chemical  reactions  can 
only  be  explained  on  this  supposition,  the  theory  of  elec- 
trolytic dissociation  finds  its  principal  support  in  the  fact 
that  all  the  different  methods  give  concordant  results  for 
the  degree  of  dissociation.  At  the  present  time  it  is 
impossible  for  the  electrochemist  to  do  without  the  theory 
of  electrolytic  dissociation. 

To  illustrate  these  facts  we  give  the  following  table  of 
measurements.  The  numbers  state  how  many  molecules 
are  formed  from  one  molecule  of  the  dissolved  salt  as 
the  result  of  electrolytic  dissociation. 

The  question  now  comes  up:  "  What  is  the  nature  of 
this  separation?"  It  cannot  be  an  ordinary  separation, 
since  the  union  of  atoms  in  forming  a  compound  is 
generally  accompanied  by  a  great  production  of  energy. 
On  decomposition  this  energy  would  have  to  appear  again, 
which  is  apparently  not  true  in  this  case.  It  seems, 
therefore,  that  the  chemical  affinity  which  has  brought 
about  the  union  of  the  atoms  has  been  compensated  for 
in  some  way  so  that  the  atoms  are  at  liberty  to  separate, 


THEORY  OF  ELECTROLYTIC  DISSOCIATION. 


49 


DEGREE  OF  DISSOCIATION  AS  DETERMINED  BY  OSMOTIC  AND  ELEC- 
TRICAL METHODS. 


Salts 

Concentra- 
tion 

Degree  of  Dissociation 

Osmotic 

Freezing- 
point 

Conductivity 

KC1.  . 
NH4C1  
Ca(N08)2  
K4Fe(CN)6.  .  . 
MgS04  
LiCl 

o.  14 
o.  148 
0.18 

o-356 
0.38 
0.13 
0.18 
o.  19 
0.184 
0.188 
0.0018 

i.  si 

1.82 
2.48 
3-°9 
i-25 
1.92. 
2.69 
2.79 
2.78 

2.47 

I  .20 
1.94 
2.52 

2.68 

2.67 
2.56 

5-92 

1.86 
1.89 
2.46 
3-°7 
i-35 
1.84 

2-51 
2.48 
2.42 
2.41 

SrCl2  - 

MgCl2.  . 

CaCl2  
CuCl2  

Na6C12O,2  .... 

Because  of  the  electromotive  effects  and  the  conductivity 
we  assume  that  the  chemical  affinity  has  been  changed  to 
an  electrical  affinity,  in  that  the  atoms  take  on  charges  of 
positive  and  negative  electricity.  The  neutral  compound 
dissociates  into  positively  and  negatively  charged  atoms 
or  radicals,  which  are  known  as  "  ions." 

In  what  follows  we  will  review  briefly  the  history  of  the 
theory,  and  at  the  same  time  explain  the  different  con- 
ceptions which  have  been  introduced. 

History  of  Electrochemistry.     The  Theory  of  Electrolytic 
Dissociation  and  its  Foundations. 

In  order  to  understand  the  foundation  of  the  theory 
and  its  advantages — a  theory  which  at  present  is  an  in- 
dispensable part  of  theoretical  chemistry — we  will  follow 
its  development  historically.  We  will  not,  however, 
confine  ourselves  strictly  to  the  history  of  the  theory  of 


50  ELECTROCHEMISTRY. 

electrolytic  dissociation,  but  will  also  take  up  that  of 
electrochemistry  in  general  and  use  this  opportunity 
to  learn  some  of  the  important  laws  of  electrochemistry. 

The  dissociation  theory  has  met  with  more  opposition 
than  most  theories  of  a  purely  hypothetical  nature, 
probably  because  at  first  sight  it  seems  to  clash  with 
our  "  chemical  sense."  But  is  not  the  atomic  theory — 
that  matter  is  divisible  until  the  final  indivisible  particles 
known  as  atoms  are  reached — still  more  antagonistic  to 
our  "  chemical  sense  "  ?  And  yet  we  find  ourselves  quite 
at  ease  where  the  atomic  theory  is  concerned.  Possibly 
the  reason  for  this  is  that  the  physical  and  nathematical 
knowledge  required  for  the  comprehension  of  the  dis- 
sociation theory  is  not  necessary  to  an  understanding  of  the 
atomic  theory.  We  are  probably  justified  in  saying  that 
most  of  the  opponents  of  the  theory  of  electrolytic  dis- 
sociation refrain  from  accepting  it  on  grounds  of  con- 
servatism— which  is  simply  another  name  for  inertia — 
while  others  oppose  it  as  they  do  the  atomic  theory, 
because  they  are  unwilling  to  accept  anything  which  they 
have  not  seen  c.  tested  by  experiment. 

The  dissociation  theory  had  its  beginning  a  long  time 
ago.  Nicholson  and  Carlysle  *  found,  and  Davy  f 
confirmed  the  facts  accurately,  that  solutions  which 
conduct  do  not  remain  unchanged  by  the  passage  of  the 
current,  as  the  metals  do,  but  are  decomposed;  that  is, 
the  chemical  affinity  which  has  brought  about  the  union 
of  the  elements  in  the  salt  is  simply  overcome  by  the 
action  of  electricity. 

The  fact  that  the  products  of  the  decomposition  are 

*  Nicholson,  Journ.  of  Nat.  Phil.,  4,  179  (1800). 
t  Gilbert's  Ann.,  7,  114,  28,  i  and  161  (1808). 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.          51 

attracted  to  the  electrodes,  where  they  are  deposited, 
proves  that  they  were  already  electrically  charged  before 
deposition,  as  otherwise  there  would  be  no  attraction; 
and  further,  the  elements  which  move  toward  the  negative 
electrode  must  be  charged  positively  and  those  which  go 
to  the  positive  electrode  must  be  negatively  charged. 

Fig.  5  is  a  facsimile  of  one  of  Faraday's  drawings  in 
which  he  has  written  the  terms  now  in  common  use. 
These  words  were  made  at  his  suggestion  by  the  philol- 
ogist Whewell.  He  called  the  negative  "  electrode " 


Fig.  5. 

the  "  cathode,"  and  this  is  the  electrode  toward  which  the 
"  cations,"  or  the  metallic  elements  in  the  "  electrolyte," 
move;  the  "  anode  "  is  the  electrode  toward  which  the 
"  anions  "  move.  The  whole  process  was  named  "  elec- 
trolysis." *  f 

About  1833,  Faraday  discovered  the  law  of  equivalent 
deposition,  now  generally  known  as  Faraday's  law.  He 

*  Faraday's  spelling  of  "cathion"  is  wrong.  The  word  anode  is 
derived  from  the  Greek  words  dvd=up  and  o<5oS=road;  cathode  is 
ro~n  Kard=  down  and  66 oS  (the  th  in  this  case  comes  from  the  aspirate 
in  oSo1*).  The  word  ion  is  from  ^eyai=to  go,  and  the  corresponding 
words  are  cation  and  anion.  Cation  should  have  no  h. 


$2  ELECTROCHEMISTRY. 

showed:  ist,  that  the  amount  of  the  electrolyte  which 
is  decomposed  is  proportional  to  the  quantity  of  electricity 
which  has  passed  through  the  solution;  and  2d,  that 
when  the  same  current  is  passed  through  two  different 
electrolytes  the  amounts  of  the  different  substances  set 
free  are  chemically  equivalent. 

ILLUSTRATION:  This  law  can  be  expressed  as  follows: 
Equal  quantities  of  electricity  precipitate  equal  quantities 
of  all  substances  in  electrolysis.  By  equal  quantities 
of  substances  is  meant  not  equal  quantities  in  grams  but 
in  gram  equivalents.  A  current  of  i  ampere  precipitates 
per  second  0.01036  milligram  equivalents  of  any  substance; 
for  instance  (cf.  table  on  p.  163): 

107.93X0.01036  =  1.118  mgr.  of  silver, 
or  35.45X0.01036  =  0.368  mgr.  of  chlorine, 

or  127  X  0.01036  =  1.3  1  6  mgr.  of  iodine, 

or  i4.o4  +    Xi6)Xo.oio36  =  o.643  mgr.  of  NO3. 


In  the  case  of  substances  whose  valence  is  greater  than 
i  we  must  divide  the  atomic  weight  by  the  valence. 
One  ampere-second  deposits 

61.6 

-^—  X  0.01036  =  0.32  94  mgr.  of  copper, 


or 


(32.06+4X16)  ,  ^^ 

—  —  Xo.oio36  =  o.5  mgr.  of  SO4, 

or  —  X 0.01036  =  0.0935  mgr.  of  Al. 

3 

Since  the  precipitation  of  metals  or  radicals  is  governed 
by   the   law   of   equivalents,   it   follows  that   equivalent 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.          53 

quantities  of  different  compounds  are  decomposed  by  one 
and  the  same  quantity  of  electricity.  Thus  i  ampere- 
second  decomposes 

—  Xo.oio36  =  0.0933  mgr.  of  water, 


or 


Since  i  ampere-second  deposits  0.01036  mgr.  equiva- 
lents or  0.00001036  gr.  equivalents,  it  is  seen  that  96  540 
ampere-seconds  are  required  to  deposit  i  gr.  equivalent; 
or  since  i  ampere-second  =  i  coulomb,  96  540  coulombs 
are  required.  This  fact  proves  that  one  equivalent  of 
each  and  every  ion  carries  the  same  charge  of  electricity. 
Faraday's  law  applies  not  only  to  water  solutions,  but 
also  to  solutions  in  other  solvents,  and  to  salts  in  a  fused 
state,  and  holds  for  all  temperatures. 

The  fact  that  the  decomposition  products  of  the  electro- 
lyte, as  hydrogen  and  oxygen,  appear  at  points  some 
distance  apart,  caused  at  first  a  great  deal  of  difficulty. 
It  was  evident  that  the  two  products  could  scarcely  be 
derived  from  the  same  molecule  of  water  or  dissolved 
substance,  but  must  come  from  different  ones.  Several 
theories  were  at  first  proposed  to  account  for  the  facts; 
for  instance,  the  theory  that  the  two  substances  hydrogen 
and  oxygen  were  not  derived  from  the  water  at  all;  that 
electricity  itself  was  nothing  less  than  an  acid. 

Von  Grotthus  *  attempted  to  clear  up  the  difficulty. 
He  assumed  that  the  anion  which  was  being  deposited 
came  from  the  molecule  which  was  nearest  to  the  anode; 

*  Ann.  d.  chem.  u.  Physik,  58,  64  (1806),  63,  20  (1808). 


5  4  ELEC  TROCHE  MIS  TR  Y. 

the  cation  which  was  being  deposited  came  from  the 
molecule  nearest  to  the  cathode.  Just  at  the  instant 
when  these  were  deposited  on  the  electrodes  the  re- 
mainder of  the  decomposed  molecule  appropriated  the 
atom  or  radical  it  had  lost  from  its  neighboring  molecule, 
this  in  turn  robbing  its  next-door  neighbor.  This  view 
was  also  apparently  held  by  Faraday. 

The  first  to  point  out  the  shortcomings  of  this  theory 
was  Grove.*  From  his  study  of  the  oxygen-hydrogen 
cell,  which  derives  its  energy  from  the  union  of  these  two 
elements,  he  concluded  that  a  decomposition  of  the  water 
molecules  is  not  necessary  for  the  evolution  of  oxygen  and 
hydrogen,  but  that  the  molecules  are  present  from  the 
start  in  a  decomposed  state. 

Clausius  f  then  followed  up  this  idea :  if  a  force  is 
necessary  to  decompose  the  molecules,  electrolysis  should 
not  be  possible  at  very  low  voltages.  But  the  electrolysis 
of  silver  nitrate  between  silver  electrodes  takes  place  at 
voltages  which  are  far  below  the  voltage  which  corresponds 
to  the  energy  of  formation  of  silver  nitrate;  that  is,  we 
decompose  at  the  expense  of  a  small  amount  of  work  a 
salt  which  is  formed  with  the  liberation  of  a  great  deal  of 
energy,  a  fact  which  conflicts  with  the  principle  of  the 
conservation  of  energy.  Clausius  concludes  therefore 
that  "  the  supposition  that  the  components  of  the  mole- 
cules of  an  electrolyte  are  firmly  united  and  exist  in  a 
fixed  orderly  arrangement  is  wrong." 

A  few  years  earlier  Williamson  {  had  expressed  a 
somewhat  similar  view.  He  proposed  the  hypothesis 

*  Phil.  Mag.,  27,  348  (1845). 

f  Poggendorf's  Ann.,  101,  338  (1857). 

J  Liebig's  Ann.,  77,  37  (1851). 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  55 

that  in  hydrochloric  acid  "  each  atom  of  hydrogen  does 
not  remain  quietly  attached  all  the  time  to  the  same  atom 
of  chlorine,  but  that  they  are  continually  exchanging 
places  with  one  another."  If  this  is  the  case,  then  the 
two  radicals  must  be  present  separately  for  a  certain 
length  of  time,  and  this  time  will  be  longer  the  farther 
apart  the  molecules  are,  or,  in  other  words,  the  more  dilute 
the  solution  is. 

This  hypothesis  was  adopted  by  Clausius,  but  at  that 
time  no  experimental  means  were  known  for  determining 
how  much  of  the  electrolyte  was  dissociated,  or,  in  other 
words,  to  determine  the  ratio  of  the  time  during  which  the 
molecules  were  dissociated  to  the  time  during  which  the 
atoms  remain  united. 

About  this  time  Hittorf's*  importantwork  was  published. 
Hittorf  found  that  during  electrolysis  changes  of  concen- 
tration occur  at  the  anode  and  cathode,  and  concluded 
that  these  changes  could  only  be  explained  by  assuming 
that  the  anions  and  cations  move  with  a  different  velocity. 
At  the  same  time  Kohlrausch  discovered  the  lawf  of  the 
"  independent  wandering  of  the  ions."  He  found  that 
in  dilute  solutions  the  conductivity  of  a  given  salt  is 
additively  composed  of  two  values  which  are  peculiar 
to  the  different  ions;  that  is,  the  potassium  ion  plays  the 
same  part  in  conducting  the  current  whether  it  is  present 
with  the  chlorine  ion  or  the  NOs  ion.  If  we  add  to  the 
conductivity  of  the  potassium  ion  that  of  the  chlorine  ion, 
which  is  also  independent  of  the  nature  of  the  cation 
present  with  it,  we  obtain  the  conductivity  of  potassium 
chloride.  This  result  shows  that  any  one  ion  troubles 

*  Ostwald's  Klassiker,  Nos.  21  and  23. 
i        f  See  the  chapter  on  Conductivity. 


5^  ELECTROCHEMISTRY. 

itself  very  little  about  the  nature  of  any  other  ions  which 
may  also  be  present  in  the  solution. 

Electrochemical  theories  had  reached  this  point  when 
van't  Hoff  in  his  classic  work  applied  the  gas  laws  to 
solutions.  We  saw  (pp.  20  and  46)  that  the  gas  laws  no 
longer  hold  when  we  consider  a  salt  whose  solution  con- 
ducts the  electric  current.  If  p  is  the  osmotic  pressure  and 
v  the  dilution,  i.e.,  the  volume  in  which  a  gram-molecule  is 
contained,  then  pv  =  RT  for  non-conducting  solutions 
(cf.  p.  26).  In  the  case  of  conducting  solutions  van't 
HofT  found  it  necessary  to  multiply  RT  by  a  factor  i,  so  that 
for  this  class  of  solutions  p-v  =  iRT. 

Arrhenius  calculated  from  Kohlrausch's  measurements 
that  only  a  part  of  the  total  number  of  molecules  of  a 
dissolved  salt  is  active  in  conducting  the  current,  and 
that  this  part  is  i  —  i;  i.e.,  if  2  =  1.7,  then  70%  of  the  total 
dissolved  salt  takes  part  in  conduction.  Arrhenius  then 
concluded:  "  If  we  must  assume  that  free  ions  are  present 
in  the  solution,  as  Clausius  and  Williamson  have  shown, 
and  if  the  osmotic  and  other  methods  show  that  many 
more  molecules  seem  to  be  present  in  the  solution  than 
we  have  introduced,  then  we  may  assume  that  the  salt  is 
dissociated,  not  as  Clausius  believed,  to  a  very  slight 
extent,  but  to  such  a  large  extent  that  this  will  account 
for  the  deviation  from  the  van't  HofT  gas  laws."  Now, 
since  only  a  part  of  the  dissolved  salt  and  not  the  whole 
is  active  in  conduction,  and  since  this  part  corresponds 
to  the  extra  molecules  which  van't  Hoff  has  shown  to 
be  present,  Arrhenius  drew  the  conclusion  that  the 
electrolyte  is  dissociated  into  ions,  the  amount  of  disso- 
ciation depending  on  the  concentration  of  the  solution 
and  nature  of  the  salt,  and  that  the  ions  are  the  only 


^E 


IV:RSITY  ) 

OF  J 

OF  ELECTROLYTIC  DISSOCIATION.          57 


active  agents  in  conducting  the  current.  This  theory 
has  become  indispensable  to  electrochemistry,  and  has 
also  become  of  great  help  in  our  understanding  of  general 
chemistry. 

When  we  bring  ordinary  salt  in  contact  with  water, 
it  dissolves,  but  at  the  same  time  the  reaction  * 


takes  place.  This  is  the  equation  of  an  ordinary  chemical 
reaction  and  like  all  reactions  finally  reaches  a  condition 
of  equilibrium.  In  the  case  of  a  normal  solution  of  NaCl, 
the  reaction  goes  on  till  67%  of  the  salt  has  dissociated 
into  ions,  i.e.,  the  degree  of  dissociation  is  67%.  Such 
a  reaction  must  follow  the  law  of  mass  action  (p.  35). 
If  x  represents  that  part  of  a  gram-molecule  which  is 
dissociated  when  the  volume  of  the  solution  is  v  (in  the 
above  case  #  =  0.67),  then  at  equilibrium  the  concentration 

T   /y* 

of  the  undissociated   molecules  will  be  -    — ,   but   the 

v    ' 

oc 

concentration  of  each  kind  of  ions  will  be  -  and  the  law 

v 

of  mass  action  requires 

T—x     #2 

'  4.  =~^2' 


*  The  ions  were  formerly  denoted  by  Na  and  Cl  to  indicate  that  we 
have  to  do  with  a  positively  charged  sodium  ion  and  a  negatively  charged 
chlorine  ion;  substances  whose  valence  is  greater  than  i  were  denoted 

+  + 

by  Cu  and  SO4,  indicating  that  the  copper  or  SO4  ions  carry  twice  the 
charge  of  the  sodium  or  chlorine  ions.  For  typographical  reasons  it 
has  become  customary  to  replace  the  +  by  •  and  the  —  by  ' ,  printed 
above  and  to  the  right  of  the  symbol. 


5  3  ELECTROCHEMISTRY. 

\ 

or,  in  general,  if  Q  is  the  concentration  of  the  ions  and  cs 
that  of  the  undissociated  molecules,  then 


n  being  the  number  of  ions  which  results  from  the  disso- 
ciation of  i  molecule  of  the  salt.  K  is  called  the  "  disso- 
ciation constant  "  of  the  salt. 

The  following  examples  will  show  how  the  dissociation 
occurs  : 

AgN03  ^  Ag'+NCV;      Na2SO4  <=±  Na'  +  Na'  +  SO4"; 


But  "  dissociation  by  steps  "  may  also  occur,  as: 
BaCl2<=±BaCl- 


In  many  cases  we  cannot  decide  from  the  formula  of  a 
salt  how  it  will  dissociate.  In  the  case  of  KHSO4  the 
following  reactions  are  possible: 


or 

KHSO4<=±K' 
or 

KHSO4<=±H' 

By  measuring  the  "  transport  number  "  we  can  generally 
determine  what  the  ions  are,  and  Hittorf  has  applied  this 
method  in  a  number  of  cases  where  the  composition  of 
the  ions  was  doubtful.  If  we  put  some  potassium  silver 
cyanide  KAg(CN)2  at  the  bottom  of  a  U  tube  and  pour 


THEORY   OF  ELECTROLYTIC  DISSOCIATION.          59 

water  into  each  arm  of  the  tube,  the  cations  will  move 
to  the  cathode  and  the  anions  to  the  anode  when  a  current 
is  passed  through  the  tube.  After  the  current  has  passed 
for  some  time  we  find  on  analyzing  the  contents  of  each 
half  of  the  tube  that  no  silver  has  wandered  toward  the 
cathode,  but  has  gone  in  the  opposite  direction  toward  the 
anode.  This  shows  that  the  silver  forms  part  of  the 
anion,  and  that  the  dissociation  occurs  thus  : 


In  a  similar  way  it  has  been  shown  that  the  chromium 
in  the  chromates  belongs  to  the  anion  just  as  sulphur 
belongs  to  the  SO  4  ion.  In  the  case  of  many  acid  salts, 
provided  the  solution  is  not  too  dilute,  the  hydrogen 
goes  as  part  of  the  anion  to  the  anode.  Acid  potassium 
sulphate  then  would  dissociate 


It  must  not  be  understood,  however,  that  no  further 
dissociation  takes  place.  In  the  above  instance  of 
KAg(CN)2  the  dissociation  constant  K  of  the  reaction 


[KAg(CN)2] 


has  a  very  large  value,  and  the  dissociation  is  nearly 
complete.     On  the  other  hand  the  dissociation  constant 

[Ag-][CN'f 
Al     [Ag(CN)2'] 

*  The  concentration  of  a  substance  is  denoted  by  enclosing  its  sym- 
bol in  brackets. 


60  ELECTROCHEMISTRY. 

of  the  reaction  Ag(CN)2'  <=*  Ag-  +  CN'  +  CN'  is  very 
small,  so  that  this  second  dissociation  only  takes  place 
to  an  exceedingly  small  extent.  In  such  a  solution  we 
have  very  many  potassium  ions  and  "  complex  "  silver- 
cyanogen  ions,  but  free  silver  ions  and  cyanide  ions 
are  present  in  exceedingly  small  amounts.  It  follows 
therefore  that  the  current  is  conducted  almost  entirely 
by  the  potassium  and  complex  ions,  while  the  others 
on  account  of  their  scarcity  are  practically  without 
effect  on  the  conductivity.  As  a  result  we  find  in  the 
above  experiment  no  silver  in  the  cathode  arm  of  the 
U  tube. 

Some  other  typical  forms  of  dissociation  are: 

Aids  <=*  Al-  '  '  +  Cl'  +  Cl'  +  Cl', 


'*  K6Fe2(CN)i2  +±  K'  +  K'-f  K• 


From  one  molecule  of  potassium  ferricyanide  seven  ions 
are  formed,  and  the  dissociated  part  has  seven  times  as 
great  an  effect  on  the  osmotic  pressure  or  lowering  of  the 
freezing-point  as  the  simple  molecules.  Other  typical 
examples  will  be  given  in  the  following  chapters. 

*  This  equation  seems  to  the  translator  to  be  incorrect,  as  Ostwald's 
"Basicity  Rule"  shows  ferricyanic  acid  to  be  tribasic.  See  Jahn, 
Grundriss  der  Elektrochemie,  2d  edition,  p.  146. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.          61 


Applications  of  the  Dissociation  Theory  in  Chemistry. 

In  this  chapter  we  cannot  enter  into  details  but  must 
limit  ourselves  to  a  few  examples  which  will  show  the 
usefulness  of  the  theory  of  electrolytic  dissociation  and 
how  we  can  apply  it  in  our  work  and  calculations.  At 
the  same  time  we  will  touch  on  a  number  of  physico- 
chemical  questions,  a  clear  understanding  of  which  is 
necessary  to  our  further  study  of  electrochemistry. 

The  supporters  of  the  theory  of  electrolytic  dissociation 
assume  that  most  of  the  reactions  of  inorganic  chemistry, 
which,  in  comparison  to  organic  reactions,  take  place  in 
a  very  short  space  of  time,  are  reactions  between  the  ions. 
The  precipitation  of  silver  chloride  from  a  silver-nitrate 
solution  by  ordinary  salt  was  formerly  explained  by  the 
following  equation: 

AgN03+NaCl  <=>  AgCl+NaN03. 

If  we  assume  that  all  the  salts  except  the  solid  AgCl  are 
dissociated  into  their  ions  the  reaction  becomes 


or  subtracting  those  ions  which  occur  on  both  sides  of 
the  equation, 

Ag'  +  CF^AgCl. 

The  essential  reaction  is  the  union  of  silver  ions  and 
chlorine  ions  to  form  insoluble  silver  chloride.  The  old 
explanation  that  "  chlorine  and  silver  react  in  solution 
to  form  silver  chloride"  is  not  strictly  correct.  In  terms 


62  ELECTROCHEMISTRY, 

of  the  theory  of  electrolytic  dissociation  "  chlorine  ions 
and  silver  ions  can  only  exist  together  in  a  water  solution 
in  very  small  concentrations;  if  the  product  of  their 
concentrations,  measured  in  mols  per  litre,  should 
exceed  i.2Xio~10  solid  silver  chloride  is  deposited  until 
the  product  of  the  concentration  of  the  ions  is  reduced 
to  this  value." 

Chloroform,  for  instance,  contains  no  chlorine  ions, 
since  it  is  a  non-conductor  of  electricity,  and  therefore  can- 
not be  electrolytically  dissociated;  therefore  it  does  not 
precipitate  silver  chloride  from  a  solution.  The  same 
is  true  for  sodium  chlorate>  NaClOs,  which  dissociates 
according  to  the  formula 


A  solution  of  this  salt  contains  chlorate  ions,  but  no  chlorine 
ions.  In  a  solution  of  KAg(CN)2,  which  dissociates  after 
the  formula 

KAg(CN)2  ^  K'+Ag(CN)2', 

so  few  silver  ions  result  from  the  further  dissociation, 
Ag(CN)2'  <=>  Ag-  +  CN'  +  CN', 

that  they  can  remain  in  the  presence  of  a  large  amount 
of  CY  ions  without  being  precipitated.  This  accounts 
for  the  fact  that  NaCl  will  not  precipitate  AgCl  from 
a  solution  of  KAg(CN)2.  Before  the  birth  of  the  theory 
of  electrolytic  dissociation  no  satisfactory  explanation  had 
been  given. 

The  theory  explains  the  slowness  of  reactions  between 
organic   substances   on   the   ground   that   they   are   not 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  63 

dissociated  to  any  measurable  extent,  and  the  same  is 
true  of  reactions  between  solid  substances.  A  mixture 
of  solid  NaCl  and  AgNO3  from  which  water  is  carefully 
excluded  does  not  react;  but  as  soon  as  it  comes  in 
contact  with  water  the  two  salts  dissolve,  are  at  once 
dissociated  into  their  ions,  and  reaction  starts.  Salts  in  a 
state  of  fusion  are  also  dissociated  so  that  under  such 
circumstances  reaction  can  easily  take  place. 

The  old  dictum  "  corpora  non  agunt  nisi  fluida  "  is 
pretty  generally  true,  but  not  absolutely,  since  solid 
substances  do  react,  but  with  extreme  slowness. 

Among  the  salts  we  must  include  the  salts  of  the  metal 
hydrogen,  i.e.,  the  acids.  These  are  generally  very 
strongly  dissociated  in  water  solution.  Just  as  potassium 
salts  have  the  common  property  of  giving  off  -potassium 
ions,  so  all  the  acids  have  the  property  of  sending  hydrogen 
ions  into  solution,  as,  for  instance, 

HOMH'+Cl', 

or 


or 

H3PO4  <=±  H-  +  H2PO4'  «=*  H- 


Acids  like  sulphuric  acid  which  can  furnish  two  hydrogen 
ions  per  molecule  are  called  dibasic,  those  which  can 
furnish  three  hydrogen  ions  tribasic,  etc.  The  examples 
just  given  show  that  the  dissociation  of  a  molecule  is  not 
necessarily  complete  but  may  take  place  by  stages,  or 
"  stepwise." 

The  bases  are  also  to  be  reckoned  among  the  strongly 


64  ELECTROCHEM1S  TR  Y. 

dissociated  salts.  Just  as  a  common  characteristic  of 
the  chlorides  is  their  ability  to  furnish  chlorine  ions,  so 
the  bases  have  the  common  property  of  furnishing 
hydroxyl  or  OH  ions.  Acids  and  bases  therefore  are 
simply  two  particular  kinds  of  salts.  Their  exceptional 
importance  in  chemistry  due  to  the  fact  that  their  char- 
acteristic ions  are  also  the  ions  of  the  most  universal 
solvent,  water.  A  chemical  science  based  on  a  solvent 
which  contained  neither  H*  nor  OH'  ions  would  there- 
fore be  wholly  unable  to  distinguish  acids  or  bases  from 
salts.  We  thus  arrive  at  a  now  and  exact  definition  of 
an  acid  or  a  base.  Acids  are  salts  which  are  capable  of 
forming  H*  ions  in  solution;  bases  are  salts  which  furnish 
OH'  ions. 

We  must  now  consider  the  dissociation  of  water,  which 
is  one  of  the  most  important  results  of  the  dissociation 
theory  and  the  most  convincing  proof  of  its  value.  We 
can  consider  water  as  a  dibasic  acid  which  dissociates 
as  follows: 


or  also  as  a  mon-acid  base,  since  it  can  furnish  OH'  ions. 
The  second  step  of  the  acid  dissociation  which  gives  rise 
to  O"  ions  is  very  slight,  i.e.,  the  concentration  of  O" 
ions  is  exceedingly  small. 

The  first  dissociation  of  water  into  H*  and  OH'  is  also 
very  slight  but  of  very  great  chemical  importance.  The 
reaction 


like  every  other  chemical  reaction  is  governed  by  the  law 
of  mass  action,  thus: 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  65 

The  equilibrium  constant  K  is  known  as  the  "  dissociation 
constant  of  water."  (Enclosing  a  symbol  in  brackets  is 
the  conventional  way  of  indicating  the  concentration  of 
a  substance.) 

Now,  the  dissociation  of  water  is  very  slight,  so  that  the 
active  mass  of  water  is  practically  unchanged  by  the 
dissociation,  and  we  may  therefore  consider  it  a  constant 
and  include  it  along  with  the  reaction  constant  without 
causing  any  appreciable  error  ;  then 


where  k  is  the  product  of  the  concentrations  of  both  ions. 
In  neutral  water  neither  H'  nor  OH'  is  present  in  excess. 
The  two  concentrations  are  equal,  so  that  if  CQ  repre- 
sents the  concentration  of  either  ion  in  neutral  water, 


The  last  equation  but  one  must  always  hold,  no  matter 
what  the  concentrations  of  H*  or  OH'OH'  may  be,  i.e., 
whether  the  solution  is  acid,  neutral,  or  alkaline.  A 
number  of  different  methods  which  we  will  consider  in 
the  following  have  given  io~7  as  the  value  of  CQ  at  about 
22°.  Therefore 

[H'][OH']=io-14. 

In  an  alkaline  solution,  which  contains'  17  grams  of  OH 
ions  per  litre,  [OH']=i,  and  [H']  must  then  be  io~14;  in 
such  a  solution,  then,  we  would  have  a  concentration  of 
i  gr.  of  hydrogen  ions  in  100  billion  litres.  In  a  o.ooi 
ormal  acid  solution  [H']  =  .ooi  and  [OH']  =  io~n,  etc. 

A  further  application  of  this  formula  is  as  follows:  if 
we  mix  i  mol  of  HC1  and  i  mol  of  NaOH  in  a  litre 
of  water,  the  product  [H']X[OH']  at  first  will  be=i,  a 


66 


ELEC  TROCHE  MIS  TR  Y. 


much  larger  value  than  is  possible.  H"  and  OH7  will 
therefore  combine  till  the  value  of  [H'j  [OH']  becomes 
io~14.  The  equations  for  this  and  other  simple  reactions 
of  neutralization  are: 

Na'  +  OH'+H'  +  Cl'   =  H20+Na-  +  Cl', 


After  subtracting  the  ions  which  appear  on  both  sides 
there  remains  in  every  case 


The  process  of  neutralization  therefore  is  always  based 
on  the  same  fundamental  reaction,  provided  of  course 
that  the  reacting  base  and  acid  are  in  a  solution  so 
dilute  that  they  are  both  completely  dissociated  into 
their  ions.  As  a  result,  the  heat  of  reaction  of  every 
neutralization  must  always  be  the  same,  and  must  be 
independent  of  the  nature  of  the  particular  acid  or  base 
used.  This  fact  has  long  been  known,  but  previous  to 
the  evolution  of  the  dissociation  theory  no  satisfactory 
explanation  had  been  given.  The  following  table  gives 
some  experimental  results: 


Acid  and  Base. 

Heat  of 
Neutralization. 

Hydrochloric  ac 
Hydrobromic 
Nitric 
Hydroiodic 
Hydrochloric 

i  ( 
1  1 

id  ai 

id  sodium  hydn 
<  < 

t  ( 

C  ( 

lithium 
potassium 
barium 
calcii'm 

3xide  .... 

13  700 
13  700 
I3  700 
13800 
I3  700 
13800 
13800 
13  900 

THEORY  OF  ELECTROLYTIC   DISSOCIATION.  67 

Hydrofluoric  acid  is  only  slightly  dissociated  in  solution, 
consequently  in  the  reaction 


HF  +  K'  +  OH'  <=>  K-  +  F'  +  H20 

HF  must  become  further  and  further  dissociated  as  the 
reaction  goes  on.  The  dissociation  of  HF  of  course 
follows  the  law  of  mass  action 

K1[HF]  =  [H'][F'] 

and  as  the  H*  ions  combine  with  OH'  ions  to  form  water 
new  ones  are  supplied  by  the  undissociated  HF.  The 
heat  evolved  by  the  dissociation  of  the  hydrofluoric  acid 
appears  as  an  excess  over  that  evolved  by  the  union  of 
H'  and  OH'.  The  neutralization  of  hydrofluoric  acid 
evolves  16  270  calories.  The  difference  between  this  and 
the  ordinary  heat  of  neutralization,  16  270  —  13  70x3  =  2  570, 
is  the  heat  of  dissociation  of  HF. 

The  question  now  arises,  when  either  the  acid  or  base 
has  a  very  small  dissociation  constant,  how  will  this  affect 
the  neutralization?  Like  all  chemical  reactions,  that 
of  neutralization  goes  on  till  a  particular  condition  of 
equilibrium  is  reached.  When  we  mix  solutions  of 
NaOH  and  HC1,  they  do  not  combine  completely  to  form 
NaCl,  some  free  NaOH  and  HC1  remain,  but  their 
quantity  is  so  small  that  it  cannot  be  measured.  The 
incompleteness  of  some  reactions  of  neutralization, 
however,  can  be  measured,  as,  for  instance,  that  of  acetic 
acid. 

From  conductivity  measurements,  or,  better,  from  the 
influence  of  sodium  acetate  on  the  velocity  of  the  saponifi- 


68  ELECTROCHEMISTRY. 

cation  of  methyl  acetate,*  it  has  been  found  that  a  mixture 
of  o.i  N  acetic  acid  and  o.i  N  sodium  hydroxide  combine 
to  the  extent  of  99.992%,  i.e.,  0.008%  of  NaOH  and 
CH3COOH  remain  in  a  free  state.  We  may  now  ask, 
is  it  possible  to  calculate  this  percentage  of  free  acid  or 
hydroxide  from  the  dissociation  constant  of  acetic  acid? 
A  o.i  N  solution  of  sodium  acetate  in  H2O  must  be 
decomposed  into  free  acid  and  base  to  exactly  this  same 
amount  (0.008%)  and  this  decomposition  of  a  salt  by 
water  is  known  as  "  hydrolysis."  The  calculation  of  the 
dissociation  constant  of  organic  acids  from  the  dissociation 
constant  of  water  and  the  degree  of  hydrolysis  of  the  salts 
of  the  acid,  or  the  reverse,  has  recently  become  of  such 
importance  for  organic  chemistry  that  we  will  give  a 
numerical  illustration  of  the  method  to  be  followed. 

The  Hydrolysis  of  sodium  acetate:    acetic  acid  disso- 
ciates according  to  the  equation 

CH3COOH  <=±  H-  +  CH3COO', 
and  the  constant  of  the  reaction  is  given  by 

'  K![CH3COOH]  -  [IT]  [CH3COO']. 

From  conductivity  measurements  the  value  of  KI  has 
been  found  to  be  0.000018.  The  relation  between  [H*] 
and  [OH']  is  governed  by  the  dissociation  constant  of 
H20,K2,  at  25°: 


*  The  velocity  of  this  reaction  is  proportional  to  the  concentration 
of  th6  OH'  ions  present,  which  accelerate  the  saponincation  catalyt- 
ically. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.          69 

Further,  there  must  be  just  as  many  positive  ions  present 
in  the  solution  as  there  are  negative  ions,  i.e., 

[H-]  +  [Na-]  =  [CH3COO']  +  [OH']. 

The  two  sodium  compounds  present,  NaOH  and 
CH3COONa,  can  be  considered  as  completely  dissociated 
at  this  degree  of  dilution,  i.e.,  practically  all  the  sodium  is 
present  in  the  form  of  Na'  ions.  This  concentration  is 
then  o.i  N,  since  we  took  that  much  Na  in  the  form  of 
sodium  acetate.  Finally  we  must  remember  'that  the 
amounts  of  NaOH  or  CH3COOH  which  do  not  combine 
in  the  reaction  of  neutralization  or  which  are  set  free  by 
the  hydrolysis  are  equal.  Since  the  NaOH  is  completely 
dissociated,  while  the  CH3COOH  is  only  dissociated  to 
such  a  small  amount  that  its  total  concentration  is  not 
appreciably  affected,  we  may  consider 

[OH']  =  [CH3COOH]. 

We  ha^e  then  four  equations  : 

(1)  o.ooooi8[CH3COOH]  =  [CH3COO'][H']. 

(2)  [H'][OH']=i.2Xio-14. 

(3)  [H-]  +  [Na']  =  [H-]  +  o.i  =[CH3COO']+[OH']. 

(4)  [CH3COOH] 


Substituting  the  value  of  [CH3COO'J  from  (3)  in  equation 
(i)  gives 

o.ooooi8[CH3COOH]  =  [H']([H-]  +  o.i 


A  solution  of  CH3COONa  reacts  alkaline;    there  must 
therefore  be  more  OH'  than  H'  present,  so  that  [H*]  is 


7o 


ELECTROCHEM1S  TR  Y. 


certainly  less  than  10  7.  This  value  is  so  small  that  it 
may  be  neglected  in  comparison  with  o.i  (at  the  most 
this  would  only  introduce  an  error  of  about  0.0001%). 
Substituting  the  value  of  [H*]  from  equation  (2)  and  then 
introducing  for  [OH']  its  value  from  equation  (4),  we 
finally  obtain 


-r      n    NX 


—  14 


o.ooooI8[CH3COOH]=-H3COOH](o.i-[CH3COOH]). 

On  solving  this  quadratic  equation  we  find  for  the  con- 
centration of  CH3COOH, 

[CH3COOH]  =  0.0000081. 

That  is,  of  the  o.i  CH3COONa,  0.0000081  or  0.0081% 
has  decomposed  into  free  acetic  acid  and  sodium  hydrox- 
ide; this  agrees  very  well  with  the  value  0.008  found  by 
experiment. 

We  may  also  reverse  this  process  and  from  the  ex- 
perimental value  0.008  calculate  the  dissociation  constant 
of  water.  .  In  this  way  we  find  : 

C0  =  i.iXio-7at  25°. 

The  following  table  contains  the  "  degrees  of  hydrol- 
ysis "  of  certain  salts  at  25°  when  present  in  o.i  normal 
solution  : 


Salt. 

Degree  of 
Hydrolysis. 

Sodium  carbonate  

3-17     % 

Potassium  phenolate.  .  . 

3-°5 

"          cyanide.  .  .  . 

I  .  12 

Borax  

0-5          " 

Sodium  acetate  

0.008    " 

THEORY  OF  ELECTROLYTIC  DISSOCIATION.  71 

It  is  seen  that  the  hydrolysis  may  amount  to  several  per- 
cent. It  is  well  known  that  a  solution  of  potassium 
cyanide  smells  of  prussic  acid,  which  can  only  result  from 
a  "  hydrolytic  dissociation  "  of  the  salt.  A  solution  of 
ammonium  carbonate  smells  strongly  of  ammonia;  the 
odor  in  this  case  being  due  to  the  free  NH3  resulting  from 
hydrolysis.  The  slow  evolution  of  carbon  dioxide  from 
a  solution  of  sodium  carbonate  is  another  instance.  Still 
another  example  is  the  conduct  of  certain  salts  of  bismuth, 
which  precipitate  bismuth  oxide  on  being  diluted;  in 
this  case  the  hydrolysis  is  so  great  that  the  solubility  of 
the  oxide  is  thereby  exceeded. 

Let  us  now  go  back  to  the  calculation  of  the  dissociation 
constant  of  water.  The  first  method  was  by  measuring 
the  hydrolysis  of  sodium  acetate;  a  second  method 
consists  in  measuring  the  velocity  of  the  reaction  of 
"saponifi cation. "  When  ethyl  acetate  and  sodium  hy- 
droxide are  brought  together,  sodium  acetate  and  ethyl 
alcohol  are  formed  according  to  .the  equation 

CH3COOC2H5  +  NaOH  <=>  CH3COONa  +  C2H5OH. 

In  this  reaction  the  ester  CH3COOC2H5  is  said  to  be 
saponified  by  the  base  NaOH.  The  velocity  of  this 
reaction  is  dependent  on  the  concentrations  of  the  reacting 
substances  and  is  further  catalytically  accelerated  by  the 
presence  of  H'  ions  (cf.  p.  15).  On  the  other  hand,  the 
number  of  OH'  ions  present  also  influence  the  velocity, 
and  it  has  been  found  experimentally  that  the  OH7  ions 
saponify  an  ester  1400  times  as  fast  as  the  H'  ions.  It 
is  easy  to  see  that  when  we  successively  diminish  the  con- 
centration of  the  OH'  ions,  the  velocity  of  the  reaction  will 
reach  a  minimum  when  the  concentration  of  the  H'  ions 


7  2  ELECTROCHEMISTRY. 

is  1400  times  as  large  as  that  of  the  OH'  ions.  If  this 
minimum  is  determined  experimentally  and  the  amount 
of  free  acid  at  that  point  determined,  we  have 


In  this  manner  van't  Hoff  has  calculated  the  dissociation 
constant  of  water,  and  obtained  as  the  value  of  c0, 

c0  =  i.2Xio~7  at  25°. 

A  third  method  for  calculating  the  dissociation  of  H2O 
consists  in  measuring  the  electromotive  force  of  the  acid- 
alkali  cell;  that  is,  of  an  element  made  of  up  two  platinum 
electrodes  saturated  with  hydrogen,  one  of  which  is  placed 
in  an  acid  and  the  other  in  an  alkaline  solution.  We  shall 
see  later  that  the  electromotive  force  of  a  metal  when 
placed  in  a  solution  of  one  of  its  salts  depends  not  only  on 
the  nature  of  the  metal  but  also  on  the  concentration  of 
the  ions  of  the  metal  present  in  the  solution  For  any 
one  metal  the  electromotive  force  varies  inversely  as  the 
logarithm  of  the  concentration  of  the  ions  of  the  metal 
in  solution.  We  may  consider  a  platinum  electrode 
saturated  with  hydrogen  as  an  electrode  of  the  metal 
hydrogen,  and  its  electromotive  force  is  therefore  depen- 
dent on  the  concentration  of  the  hydrogen  ions  in  the 
solution.  If  we  measure  the  electromotive  force  of  the 
acid-alkali  cell  and  determine  by  titration  the  concentration 
of  the  H'  ions  on  one  side  and  that  of  the  OH'  ions  on  the 
other,  we  can  calculate  from  this  result  the  concentration 
of  the  H'  ions  in  the  alkaline  solution.  In  a  normal 
solution  of  NaOH  where  the  concentration  of  the  OH' 
ions  is  nearlv  =  i  it  has  been  found  that  the  concentration 


THEORY  OF  ELECTROLYTIC  DISSOCIATION. 


73 


of  the  H*  ions  is  about   i.44Xio~14..    That  is,  in  this 
solution 

[H'][OH']=  1.44X10-1*, 


or 


The  conductivity  of  pure  water  furnishes  a  fourth 
method.  The  measurements  made  by  Kohlrausch  on 
the  purest  water  obtainable  have  given  the  following 
figures: 

co  =  o.78Xio~7  at  18° 
and 

~"7  at  25°. 


(The  method  by  which  these  results  were  obtained  will  be 
discussed  later,  in  the  chapter  on  Conductivity.)  These 
four  independent  methods  have  given  the  following  results 
for  the  dissociation  of  water: 


i.iXio"7,    i.2Xio~7,    and 


If  we  take  the  constant  for  25°  as  ^T=i.2Xio~14,  we  can 
calculate  the  value  of  the  constant  for  other  temperatures 
by  means  of  van't  Hoff's  equation,  since  the  heat  of  the 
reaction  Hv-t-OHr  =  H2O  is  13700  cal.  From  these 
results  it  has  been  calculated  that  the  conductivity  of  the 
purest  water  should  increase  5.81%  per  degree  rise  of 
temperature.  Kohlrausch  found  that  the  increase  was 
5.32%.  The  following  table  gives  the  dissociation  of 
water  at  different  temperatures  : 


Temperature  = 

0 

2 

10 

18 

26 

34 

42 

5° 
2.48 

TOO 

8-5 

c0Xio7  = 

o-35 

o-39 

0.56 

0.80 

i  .  i 

1.47 

i-93 

74  ELECTROCHEM1S  TR  Y. 

A  number  of  purely  chemical  problems  which  cannot  be 
satisfactorily  explained  without  the  help  of  the  theory  of 
equilibrium  will  be  discussed  in  the  chapter  on  Con- 
ductivity, after  we  have  learned  the  different  methods  of 
measuring  dissociation  constants.  Among  these  are: 
influence  of  the  strength'  of  acids  and  bases  on  the  saponi- 
fication  of  esters,  on  the  inversion  of  sugar,  and  on  the 
hydrolytic  dissociation  of  salts;  distribution  of  an  acid 
between  two  bases,  or  of  a  base  between  two  acids; 
rapidity  of  solution  of  metals,  carbonates,  and  oxalates 
in  acids;  the  influence  of  dissolved  salts  on  one  another, 
etc. 

The  dissociation  theory  disposes  of  the  question  whether 
a  reaction  occurs  when  solutions  of  salts  which  have 
no  common  ions  are  brought  together;  for  instance,  are 
KC1  and  NaBr  formed  when  solutions  of  KBr  and 
NaCl  are  mixed?  The  absence  of  any  evolution  or 
absorption  of  heat  would  go  to  show  that  no  reaction 
takes  place.  The  dissociation  theory  shows  that  the 
question  is  meaningless.  Before  mixing,  the  solutions 
contain  the  ions  K*,  Na',  Cl'  and  Br';  and  after  mixing,  the 
resulting  solution  contains  the  same  ions  unchanged. 
No  reaction  can  have  occurred. 

According  to  the  dissociation  theory  it  is  self-evident 
that  the  properties  of  such  mixed  solutions  are  additively 
built  up  of  the  properties  of  the  original  solutions.  The 
specific  gravity,  for  instance,  is  simply  obtained  from  the 
specific  gravities  of  the  original  solutions.  We  can  go 
one  step  farther,  since  the  specific  gravity  of  a  solution  of 
a  single  substance  is  additively  made  up  of  values  peculiar 
to  the  ions.  If  we  know  the  number  representing  the 
effect  of  each  ion  on  the  specific  gravity,  we  can  calculate 


THEORY  OF  ELECTROLYTIC  DISSOCIATION.  75 

by  simple  addition  the  specific  gravity  of  a  mixture  of 
any  ions,  i.e.,  the  specific  gravity  of  a  solution  of  any 
salt.  In  a  similar  manner  it  has  been  shown  that  the 
compressibility,  the  capillarity,  the  internal  friction, 
the  index  of  refraction,  the  magnetic  rotation  of  the  plane 
of  polarization,  and  the  light  absorption  of  solutions  are 
additive  properties.  These  few  examples  have  shown 
some  of  the  applications  of  the  dissociation  theory  to 
chemical  phenomena,  and  will  suffice  for  the  present. 
We  need  only  mention  that  the  conduct  of  indicators  in 
titration  has  been  explained  satisfactorily  by  the  dissocia- 
tion theory.  Also  many  analytical  reactions,  such  as 
the  precipitation  of  metallic  sulphides  by  hydrogen 
sulphide,  can  easily  be  understood  from  a  knowledge  of  the 
solubility  products  and  the  state  of  dissociation.  (Cf. 
chapter  on  Conductivity,  p.  103). 

Finally  a  few  words  must  be  added  on  the  application 
of  the  dissociation  theory  to  physiological  problems.  The 
theory  has  widely  increased  our  knowledge  of  the  poison- 
ous action  of  certain  classes  of  substances.  The  acids  are 
more  poisonous  and  have  a  greater  physiological  action 
according  as  their  dissociation  constant  is  great  or  small. 
The  ions  of  mercury  are  very  poisonous.  If  a  salt  con- 
taining mercury  is  taken  into  the  stomach,  the  poisonous 
effect  is  more  intense  the  higher  the  salt  is  dissociated. 
Corrosive  sublimate  is  exceedingly  poisonous,  while  the 
slightly  soluble  calomel  which  gives  rise  to  few  mercuiy 
ions  is  less  poisonous  although  physiologically  active. 
Cyanide  of  mercury,  on  the  other  hand,  which  contains 
the  two  active  poisons'  mercury  and  prussic  acid,  is  itself 
not  very  poisonous.  This  is  accounted  for  by  the  fact 
that  cyanide  of  mercury  is  practically  undissociated,  as 


7  6  cLEC  TROCHE  MIS  TR  Y. 

has  been  shown  by  conductivity  measurements.  An 
every-day  example  of  the  application  of  the  osmotic  theory 
to  physiology  is  the  following:  The  cells  of  the  human 
body  contain  dissolved  substances  and  have  therefore  a 
certain  osmotic  pressure.  When  a  wound  is  washed  with 
water,  the  cells,  whose  walls  are  "  semipermeable,"  draw 
in  water  and  burst,  giving  rise  to  continued  bleeding.  To 
avoid  this  the  wound  should  be  washed  with  a  solution 
whose  osmotic  pressure  is  the  same  as  that  of  the  solution 
in  the  cells.  Such  a  solution  is  the  2%  solution  of  boric 
acid.  If  a  2%  solution  of  NaCl  were  used,  this  would 
cause  smarting,  since  NaCl  is  completely  dissociated 
and  has  twice  the  osmotic  pressure  of  the  boric  acid, 
which  is  practically  undissociated.  A  i%  solution  of 
salt,  the  so-called  "  physiological  salt  solution,"  is  there- 
fore used  for  cleansing  wounds.  Washing  out  the  nose 
with  water  causes  pain,  but  this  may  be  avoided  by  the 
use  of  a  1%  solution  of  common  salt.  A  swimmer 
knows  that  it  is  unpleasant  to  open  the  eyes  under  fresh 
water,  but  in  sea-water,  which  has  nearly  the  same  osmotic 
pressure  as  the  solution  in  the  cells  of  the  eye,  the  eyes 
may  be  kept  open  for  a  long  time  without  smarting. 


CHAPTER  IV. 

CONDUCTIVITY. 

JUST  as  water  strives  to  descend  from  a  higher  to  a 
lower  level,  or  as  heat  tends  to  pass  from  a  higher  to  a 
lower  temperature,  so  electricity  tends  to  sink  from  a 
higher  to  a  lower  "potential."  In  these  three  cases  the 
tendency  is  greater,  the  greater  the  difference  in  level, 
or  in  "  potential,"  and  consequently  the  quantity  which 
falls  in  unit  time  is  governed  by  the  difference  of 
potential.  A  quantity  of  water  is  measured  in  litres, 
a  quantity  of  heat  in  calories,  and  a  quantity  of  electricity 
in  coulombs.  The  quantity  of  water  flowing  in  a  given 
time  is  governed  by  the  size  of  the  pipe  through  which  the 
water  flows,  as  well  as  by  the  difference  in  level.  The 
quantity  of  water  per  unit  of  time  is  greater,  the  greater  the 
cross-section  of  the  pipe;  and  smaller,  the  longer  the  pipe. 
This  quantity  can  be  measured  by  determining  the 
number  of  litres  per  unit  of  time  which  flows  in  at  the  top 
or  out  at  the  bottom  of  the  pipe.  This  same  amount  must 
also  pass  any  cross-section  of  the  pipe  in  unit  time.  The 
amount  of  water  is  further  dependent  on  the  friction  of 
the  water  against  the  material  of  which  the  pipe  is  made. 
In  other  words,  it  is  directly  proportional  to  the  reciprocal 
of  the  value  of  this  friction,  which  we  might  call  the 

77 


78  ELECTROCHEMISTRY. 

conductivity  for  water  of  the  pipe  material.  Exactly 
similar  relations  hold  for  the  conduction  of  heat  and  of 
electricity.  When  two  quantities  of  electricity  which  have 
a  different  potential  are  connected  by  a  conductor,  a 
certain  quantity  of  electricity  per  unit  of  time  will  pass 
through  the  .conductor.  This  amount  per  unit  of  time, 
or  current,  will  vary  directly  with  the  cross-section  of  the 
conductor  and  inversely  with  its  length  and  with  the 
friction  which  the  material  of  the  conductor  offers  to 
passage  of  the  electricity.  These  relations  are  expressed 
in  Ohm's  Law : 

Amount  of  electricity  in  coulombs          Eq 

Current  =  -  J  -  =  * = -i. 

.  Time  Iw 

In  this  formula  E  represents  the  impelling  electromotive 
force,  or  difference  of  potential,  q  the  cross-section  of  the 
conductor,  /  its  length,  and  w  is  a  value  which  varies  from 
substance  to  substance,  and  expresses  the  resistance  which 
each  .substance  offers  to  the  passage  of  electricity.  The 
current  is  therefore  proportional  to  the  electromotive 
force  and  the  cross-section,  and  inversely  proportional  to 
the  length  and  specific  resistance,  w  is  called  the  "  specific 
resistance  ";  it  is  the  reciprocal  of  the  conductivity  for  the 
unit  of  cross-section  and  length,  and  is  the  resistance 
which  a  cube  of  the  conductor  i  centimetre  in  thickness 
offers  to  the  passage  of  the  current.  If  we  put 'a  difference 
of  potential  of  i  volt  on  two  opposite  sides  of  this  cube 
and  find  that  the  current  flowing  is  i  ampere,  it  follows 
from  the  above  equation  that  the  specific  resistance  of  the 
conductor  is  i.  The  reciprocal  of  the  specific  resistance 
is  the  specific  conductivity.  The  specific  conductivity 


CONDUCTIVITY. 


79 


of  a  substance  is  i  when  a  difference  of  potential  of 
i  volt  will  send  a  current  of  i  ampere  through  a  cube  of 
the  substance  i  centimetre  in  diameter.  The  specific 
resistance  is  then  i  ohm. 

A  distinction  was  formerly  made  between  good,  bad, 
and  medium  conductors.  This  distinction,  however,  can- 
not be  adhered  to,  since  we  have  conductors  of  every  order 
of  magnitude.  The  following  table  gives  the  specific 
conductivity  of  a  number  of  substances : 

SPECIFIC  CONDUCTIVITY  IN  RECIPROCAL  OHMS  or  A  CENTIMETRE  CCBE 

AT  18°. 

K18  is  the  specific  conductivity;  ols=—  is  the  specific  resistance;   <718'= 

K 

10  ooo  (T18  gives  the  resistance  of  a  wire  i  metre  in  length  and  i  square 
millimetre  in  cross-section;  a  is  the  temperature  coefficient;  if  T  is  the 
temperature,  then  <7T=als[i  +  a:(T—  18)].  The  figures  apply  to  pure  soft 
metals. 


*1S- 

*» 

»«'• 

a. 

Silver            

, 

, 

Copper             

+  0.0037 

Aluminium 

587  ooo 

Zinc   

76  800 

+  0.0037 

Mercury  

10  420 

0.0000958 

o.  13 

0.958 

+  0.00092 

Manganine  
Nickeline  
Gas  carbon  *  

HoSO    30%.  . 

23  800 
23  800 

200 

o  .  000042 
o  .  000042 
o  .  0050 

0.49 

0.42 
0.42 

5° 

+  o  .  00003 
+  0.00023 
—  o  .  00003 
to 
—  o  .  00008 

Slate  *      . 

1  •  oo 
o  000014 

w.  /^ 

Wood  charcoal  *  ... 
Benzol  * 

o  .  00004 
7    eVio-10 

26  ooo 

i  300  ooo  ooc 

Hard  rubber  *  

?.5Xio-16 

4Xio15 

Approximate  values. 


Silver  is  the  best  conductor  known,  although  copper, 
which  is  used  most  extensively,  is  not  far  behind.     Alu- 


8o  ELECTROCHEMISTRY. 

minium,  which  has  lately  come  into  prominence  as  a 
material  for  power  transmission  cables,  conducts  only  about 
half  as  well  as  copper,  but  has  the  advantage  of  lightness. 
Impurities  in  a  metal  always  diminish  its  conductivity, 
consequently  all  alloys  have  a  lower  conductivity  than  the 
metals  themselves.  Thirty  percent  sulphuric  acid  has 
at  1 8°  a  conductivity  of  about  f,  at  40°  of  about  i;  i.e., 
a  centimetre  cube  of  sulphuric  acid  of  this  strength  has  a 
resistance  of  i  ohm.  A  complete  list  of  substances  could 
be  given  whose  resistances  lie  between  those  of  nickeline 
and  hard  rubber,  which  shows  that  all  degrees  of  resistance 
are  possible.  The  temperature  coefficient  of  the  resistance 
of  all  the  metals  and  most  of  the  alloys  is  positive,  i.e., 
the  resistance  increases  as  the  temperature  rises.  In  the 
case  of  practically  all  liquid  conductors  the  temperature 
coefficient  of  the  conductivity  is  positive,  and  in  the  case 
of  water  solutions  its  value  would  indicate  a  conductivity 
of  zerjo  at  about  —30°. 

It  is  impossible  to  make  a  sharp  distinction  between 
good  and  bad  conductors,  but  another  very  important 
distinction  can  be  made.  All  conducting  substances  may 
be  divided  into  two  classes :  the  first  includes  all  substances 
which  remain  unchanged  by  the  passage  of  the  current; 
in  this  class  belong  all  the  metals,  practically  all  solid 
conductors  and  a  few  liquids.  The  second  class  com- 
prises all  substances  which  are  definitely  changed  by  the 
passage  oj  the  current;  to  this  class  belong  the  electrolytes, 
i.e.,  salt  solutions  and  salts  in  a  state  of  fusion. 

The  rule  has  been  proposed  that  a  substance  shows 
metallic  conduction  when  the  temperature  coefficient 
of  its  conductivity  is  negative;  electrolytic  conduction 
hen  the  coefficient  is  positive.  This  rule,  however,  does 


CONDUCTIVITY.  8 1 

not  always  hold,  for  gas  carbon,  which  conducts  like  a 
metal,  has  a  positive  temperature  coefficient  of  conductivity 
(or  negative  temperature  coefficient  of  resistance).  Cer- 
tain solutions  show  a  negative  temperature  coefficient  of 
conductivity.  Even  among  the  metals  there  are  certain 
alloys  which  have  a  positive  temperature  coefficient  of 
conductivity. 

The  difference  between  the  two  kinds  of  conductivity 
will  be  clearer  if  we  assume  that  in  a  metallic  conductor 
the  atoms  touch  each  other,  and  there  are  everywhere 
present  bridges  over  which  the  electricity  may  pass.  In 
an  electrolyte  the  dissolved  substances  which  conduct 
the,  current  are  more  or  less  widely  separated,  so  that 
if  electricity  is  to  pass  from  one  atom  to  another  these 
atoms  must  first  traverse  a  certain  distance  in  order  to 
come  in  contact.  A  rise  of  temperature  causes  metals  to 
expand  and  thus  the  contact  between  the  atoms  becomes 
less  intimate  and  the  resistance  increases.  In  the  case  of 
electrolytes,  however,  the  rise  in  temperature  diminishes 
the  friction  to  which  the  atoms  are  subject  in  their 
motions  and  the  conductivity  increases. 

Conductivity  of  Solutions. 

In  the  study  of  electrochemistry  we  have  to  deal  princi- 
pally with  solutions  of  salts  in  water,  and  we  will  therefore 
consider  more  closely  the  mechanism  of  the  conduction  of 
electricity  through  a  solution. 

We  saw  on  p.  58  that  salts  when  dissolved  in  water 
dissociate  into  electrically  charged  ions.  When  two 
electrodes  are  connected  with  the  poles  of  a  battery  so  that 
one  is  charged  positively  and  the  other  negatively  and 
the  electrodes  dipped  into  a  solution  of  any  salt,  the. 


82  ELECTROCHEMISTRY. 

positive  electrode  exerts  an  attractive  force  on  the  nega- 
tively charged  ions  and  a  repelling  force  en  the  positively 
charged  ions,  while  at  the  other  electrode  the  positive  ions 
are  attracted  and  the  negative  repelled.  As  a  result  the 
negatively  charged  anions  move  to  the  positively  charged 
anode  and  the  positively  charged  cations  go  to  the  cathode. 
At  the  electrodes  the  ions  are  discharged;  i.e.,  they 
neutralize  a  part  of  the  electricity  with  which  the  electrodes 
are  supplied,  and  either  remain  as  neutral  matter  on  the 
electrode  or  enter  into  further  reactions.  The  charges 
on  the  electrodes  which  have  been  neutralized  by  the 
ions  are  of  course  immediately  renewed  by  the  battery. 

As  a  result  of  the  pull  exerted  on  the  ions  by  the  charges 
on  the  electrodes  the  ions  move  through  the  solution,  and 
since  -they  themselves  are  electrically  charged  they  thus 
transport  a  current  through  the  solution.  As  was  seen 
on  p.  52,  each  gram  equivalent  of  any  ion  always  carries 
the  same  amount  of  electricity,  96  540  coulombs,  i.e., 
the  anions  carry  96  540  coulombs  of  negative  electricity 
per  mol,  and  the  cations  the  same  amount  of  positive 
electricity  per  mol.  When  i  mol  of  K'  ions  and  i  mol 
of  CY  ions  pass  through  a  plane  perpendicular  to  the 
direction  of  the  current  in  one  second,  then  2  X  96  540 
coulombs  are  transported  and  the  current  strength  is 
193  080  amperes,  since  it  makes  no  difference  whether 
positive  electricity  moves  in  one  direction  or  negative  in 
the  other.  If  instead  of  i  mol  i/iooooo  mol  passes 
through  the  plane  per  second  the  current  is  only  1.931 
amperes. 

We  must  now  consider  the  all-important  question: 
What  is  the  relation  between  the  conductivity  of  an  electro- 
lyte and  the  number  and  nature  of  the  ions? 


CONDUCTIVITY.  83 

Let  us  consider  two  metallic  plates,  serving  as  electrodes, 
placed  parallel  to  each  other  at  a  distance  of  i  centimetre  ; 
between  these  we  pour  the  solution  to  be  considered. 
Since  all  the  ions  are  either  attracted  or  repelled  by  the 
electrodes,  and  since  they  all  take  part  in  transporting 
the  current,  the  conductivity  of  the  solution  will  be 
greater  the  more  i;ms  there  are  between  the  electrodes; 
two  equivalents  of  the  ions  will  give  twice  the  conductivity 
of  one  equivalent.* 

The  conductivity  will  also  depend  on  the  amount  of 
electricity  which  each  ion  can  carry;  this,  however,  is 
the  same  for  all  ions  since  they  all  carry  96  540  coulombs 
per  equivalent.  Finally,  the  conductivity  is  dependent  on 
the  velocity  with  which  the  ions  move,  i.e.,  is  conditioned 
by  the  different  degrees  of  friction  which  the  ions  must 
overcome  as  they  move  through  the  solution.  If  we 
represent  by  L  the  conductivity  of  our  solution,  by  r  the 
friction,  and  by  m  the  number  of  equivalents  present, 
then 

mX  96540 


If  we  represent  by  A  the  reciprocal  value  of  r  multiplied 
by  96  540,  then  when  m=i,  i.e.,  when  we  are  dealing  with 
i  equivalent  of  the  ions,  L  =  A.  A  is  called  the  equivalent 
conductivity.  The  equivalent  conductivity  of  a  salt  is 
therefore  equal  to  i  when  an  electromotive  force  of  i  volt 

*  "  Gram  equivalent,"  or  simply  "equivalent,"  is  the  number  of  grams 
of  the  substance  obtained  by  dividing  the  atomic  or  molecular  weight 
by  the  valence,  i.e.,  it  is  mol  (see  p.  18)  divided  by  valence.  In  other 
words,  it  is  the  weight  in  grams  of  a  substance  which  carries  a  charge 
of  96  540  coulombs.  The  atomic  weight  of  the  bivalent  element  zinc, 
for  instance,  is  65.4  and  its  equivalent  is  32.7  grs, 


84  ELECTROCHEMISTRY. 

suffices  to  send  a  current  of  i  ampere  between  two  elec- 
trodes which  are  i  cm.  apart,  when  the  solution  be- 
tween the  electrodes  contains  i  gram  equivalent  of  each 
ion  of  the  dissolved  salt.* 

In  this  definition  no  account  is  taken  of  the  volume  of 
the  solution  between  the  electrodes,  the  only  provision 
is  that  they  are  i  cm.  apart.  Whether  the  gram  equivalent 
is  present  in  a  small  or  large  volume  of  solvent  the  pull 
exerted  on  the  ions  by  the  electromotive  force  of  the 
electrodes  wrill  always  be  the  same,  and  the  same  is  true 
of  their  velocities  and  electric  charges.  What  has  just 
been  said  in  regard  to  the  salts  can  be  applied  to  each 
kind  of  ion.  The  conductivity  of  any  sort  of  ion  will  be 
high  according  as  its  concentration  is  high  and  the  less 
the  friction  is  which  the  ion  has  to  overcome  in  moving 
through  the  water. 

Let  k'  represent  the  conductivity  of  the  cation,  m'  the 
number  of  equivalents  present,  U  its  velocity  (reciprocal  of 
the  friction),  and  96  540  U  =  10',  and  let  &',  m',  V,  and  /0' 
be  the  corresponding  values  for  the  anion,  then 

Conductivity  of  the  cation    =k'  =  m'  Uq6  540  =  m'l0', 
"   "    anion     =kf  =  m'Vg6  $4o  =  m'l<f, 
"  "    "    solution  =  &  =m'l0'+m'l0'. 

In  the  solution  of  a  salt  m'  is  always  equal  to  m',  since 
the  number  of  equivalents  of  cations  must  necessarily 


*  Any  changes  at  the  electrodes  brought  about  by  the  passage  of  the 
current  and  which  may  result  in  a  back  electromotive  force  are  not  con- 
sidered in  this  definition.  This  phenomenon  of  "polarization"  will  be 
considered  later.  Any  difficulty  arising  from  this  source  can  be  avoided 
by  suitable  methods  of  measurement.  See  Book  II, 


CONDUCTIVITY.  85 

equal    the   number   of   equivalents   of   anions;     then   if 


or  if  m  =  i  (i  equivalent  in  solution), 


Each  ion,  then,  has  a  particular  value  IQ  known  as 
the  "  molecular  conductivity  of  the  ion,"  and  by  adding 
them  together  the  conductivity  of  any  salt  may  be  obtained. 

Since  the  ions  lead  a  rather  independent  life  and  any 
one  ion  bothers  itself  very  little  about  what  the  others 
may  be  doing  it  follows  that  IQ  has  the  same  value  in  all 
solutions. 

To  take  an  example,  the  conductivity  of  the  K'  ion  is 
65.3,  the  molecular  conductivity  of  KC1  is  131.2,  conse- 
quently the  conductivity  of  the  CY  ion  is  131.2  —65.3  =  65.9. 
Since  the  conductivity  of  NaCl  is  110.3,  we  nnd  that  the 
value  for  the  Na*  ion  is  no.  3—  65.9  =  44.4.  Further,  since 
the  conductivity  of  NaNOs  is  105.2  and  therefore  that  of 
NO3'  is  60.8,  the  conductivity  of  KNO3  is  65.3+60.8  = 
126.1.  This  law,  that  the  conductivity  0}  any  one  kind  of 
ion  is  independent  of  the  nature  of  the  ions  of  opposite 
.charge  which  may  be  present  in  a  solution,  was  called  by 
its  discoverer,  Kohlrausch,  the  "  law  of  the  Independent 
wandering  of  the  ions."  A  table  of  the  values  of  IQ  for  the 
different  ions  will  be  given  in  Book  II.  By  adding  the 
different  values  of  IQ  we  obtain  the  value  of  A0  for  any 
salt. 

Thus  far  we  have  considered  only  solutions  containing 
a  known  quantity  of  ions.  But  in  general  we  are  not  sure 
of  the  quantity  of  ions  present,  we  simply  know  the  total 


$6  ELECTROCHEMISTRY. 

quantity  of  salt.  As  we  saw  on  p.  48,  however,  all  salts 
are  not  entirely  dissociated  into  ions,  but  only  to  an 
extent  which  generally  represents  a  large  fraction  of  the 
whole.  This  fraction  can  be  determined  by  measure- 
ments of  the  osmotic  pressure,  or  of  the  freezing-  or 
boiling-points  of  the  solution.  Let  a  be  the  degree  of 
dissociation  for  the  concentration  y  rml  per  c.c.,  i.e., 
for  every  mol  present  a  mols  have  dissociated  into  ions 
and  the  salt  is  iooa%  dissociated.  For  every  mol  present 
then  i—  a  mols  remain  as  undissociated  salt,  and  we 
find  as  the  conductivity  of  the  solution,  not  k0  =  m(lQ'  +/o')> 
but  k  =  ma(l0'  +  l0'). 

Thus  far  we  have  not  considered  any  particular  volume 
of  solution  between  the  electrodes.     The  specific   con- 

ductivity of  our  solution  (cf.  p.  79)  is  ic  =  —  ,  where  q  is 

the  cross-section.  Since  in  this  particular  case  /  =  i,  the 
volume  of  the  solution,  v  =  q  and  k  =  KV.  Further,  the  con- 
centration in  mols  per  c.c.  is 


v 
or 


or  if  7)  =  i  mol  per  c.c., 


A^  is  called  the  equivalent  conductivity  of  the  salt  for 
the  concentration  i).  This  equation  is  used  very  often  to 
determine  the  degree  of  dissociation.  We  measure  the 
specific  conductivity  of  the  solution  and  divide  this  by 

if 

the  equivalent  concentration  of  the  solution,  i.e.,  -  =  Av  and 


CONDUCTIVITY.  87 

this  gives  the  equivalent  conductivity.  We  then  introduce 
the  values  for  /0'  and  /o'  from  the  table  mentioned  on  p. 
85  and  obtain 


A0  is  the  equivalent  conductivity  of  the  salt  when  it  is 
completely  dissociated  into  its  ions. 

From  what  has  been  said  it  is  clear  that  the  value  of 
AQ  =  IQ'  +  IQ  can  only  be  found  when  a  =  i;  that  is,  when 
all  the  dissolved  molecules  are  dissociated  into  their  ions. 
Such  solutions,  however,  do  not  exist  in  reality,  since  the 
reaction  of  dissociation  is  incomplete  and  proceeds  until 
a  state  of  equilibrium  is  reached. 

Nevertheless  the  law  of  the  independent  wandering 
of  the  ions  holds  for  solutions  when  dissociation  is  net 
complete.  Dissociation  is,  in  a  way,  an  additive  property, 
and  there  is  a  law  of  independent  dissociation  of  the  ions 
which,  while  not  as  exact  and  of  such  general  application 
as  the  other,  is  still  of  great  use  in  calculation.  It  states 
that  the  degree  of  dissociation  of  a  dissolved  substance 
may  often  be  calculated  from  numbers  which  are  peculiar 
to  each  ion.  From  the  two  laws  it  follows  that  the  values 
of  a/0*  and  a/o'  are  definite  for  a  given  concentration. 
Let  alQ'  =  lc  and  alrf  =  lc'  be  the  conductivities  of  the  ions 
at  the  concentration  c  and  we  obtain  for  the  equivalent 
conductivity  at  the  concentration  c: 


i.e.,  the  equivalent  conductivity  at  the  concentration  c  is 
equal  to  the  sum  of  the  conductivities  of  the  ions.  It 
must  always  be  kept  in  mind  that  the  degree  of  dissociation 


88  ELECTROCHEMISTRY. 

is  always  included  in  the  values  of  lc'  and  /</,  but  not  in  the 
values  of  /0*  and  IQ.  A  complete  table  of  the  values  of 
/  for  all  ions  and  for  all  concentrations  is  given  by  Kohl- 
rausch  and  Holborn.*  This  table  is  also  given  in  Book 
II  of  this  series. 

The  question  now  arises,  how  are  the  values  of 
/o  and  /  determined  experimentally?  On  measuring  the 
equivalent  conductivity  of  a  wf  KC1  solution  we  find  it  to 
be  98.2,  then 

^Kci  =  ^K  +  fa  =  98-2. 

Using  a  n  NaCl  solution  we  find 

=  ^Na  +  fa  =  74-45 


also 

=  66.  0, 


,=67.8. 

In  these  four  equations  there  are  five  unknown  quantities, 
fe,  ^Na>  ^Ag>  fa>  ^NO3,  and  without  further  data  the  single 
values  cannot  be  found.  The  fifth  necessary  equation 
is  furnished  by  measuring  the  "  transport  number,"  which 
gives  the  value  of 

V 

For  the  transport  number  of  KC1, 

fa 

IK + lei 

The  value  0.503  has  been  found  by  experiment. 

*  Kohlrausch  and  Holborn,  Leitvermogen  des  Elektrolyt.  Teubner, 
Leipzig. 

f  The  letter  n  means  "normal."  o.i  n  is  tenth  normal;  3  n  is  three 
times  normal;  etc. 


CONDUCTIVITY. 


From  this,  and  from  the  conductivity  of  a  normal  KC1 
solution,  AKCi  =  lK  +  lCi  =  ()8.2)  the  value  of  /C1  is  found  to 
be  49.4. 

With  the  help  of  this  figure  we  obtain  the  following 
values  for  the  conductivities  of  the  five  unknown  quanti- 
ties 

IK  /Cl  /Na  /N0a        /Ag 

48.8       49.4       25.0       41.0       26.8 

In  exactly  the  same  way  the  values  for  /  may  be  found 
for  other  concentrations,  for  instance,  for  o.oi  n  they  are 

61.3     62.0     40.5     56.8     51.9. 

It  must  not  be  forgotten  that  these  numbers  represent 
not  the  velocities  of  the  ions  alone,  but  the  velocities 
multiplied  by  the  degree  of  dissociation. 

In  order  to  determine  the  values  of  /0*  and  /0'  we  must 


t- 

1 


Concentration 


Dilution 


FIG.  6. 


know  the  value  of  AQ.  This  cannot  be  measured  directly, 
since  dissociation  is  complete  only  at  an  infinite  dilution. 
If  we  plot  the  value  of  A  in  its  dependance  on  the  con- 
centration we  obtain  a  curve  similar  to  Fig.  6.  In  this 
the  abscissae  represent  the  dilution  and  the  corresponding 
equivalent  conductivities  are  plotted  as  ordinates.  As 


90  ELECTROCHEMISTRY. 

the  dilution  increases  the  curve  approaches  asymptotic- 
ally a  maximum  which  we  cannot  reach  experimentally, 
but  which  may  be  found  by  extrapolation.  In  this  way 
it  is  possible  to  determine  the  value  of  AQ.  Since  the 
transport  number  remains  essentially  the  same  for  all 
concentrations  we  may  use  the  value  found  to  calcu- 
late /o, 

l0f=nA0     and     A0  —  /o'=/o". 

Pure  substances  conduct  poorly:  the  specific  con- 
ductivity of  ordinary  distilled  water  at  18°  is  about  io"6. 
But  even  this  low  conductivity  is  not  the  conductivity  of 
pure  water,  but  is  due  almost  entirely  to  small  amounts 
of  dissolved  substances.  Although  the  amount  of  these 
dissolved  impurities  may  be  so  small  as  to  escape  any 
chemical  tests,  still  they  have  a  very  marked  influence 
on  the  conductivity.  Glass  may  be  dissolved  to  a  very 
slight  extent  Dy  water,  also  carbon  dioxide  from  the  air 
when  dissolved  in  water  furnishes  ions  which  may  impart 
a  marked  conductivity  to  the  water. 

By  very  careful  distillation  and  other  methods,  Kohl- 
rausch  was  able  to  obtain  water  so  pure  that  its  specific 
conductivity  was  only  0.0384  Xio~6.  Probably  a  part  of 
even  this  low  figure  is  due  to  dissolved  impurities,  but 
in  any  case  not  a  very  large  part,  as  the  following  calcula- 
tion shows:  From  the  specific  conductivity  K  (  =  recip- 
rocal of  the  resistance  of  a  centimetre  cube  of  water)  and 
the  values  of  the  velocities  of  the  ions  H*  and  OH', 


we  obtain  as  the  number  (m)  of  H'  and  OH'  ions  in  i  c.c. 
of  this   water   m  =  o.fjSXio~w.      In    i    litre,   then,   the 


CONDUCTIVITY  91 

concentration  of  H*  and  OH'  ions  is  o.ySXio"7  at  18°. 
The  fact  that  several  other  methods  for  determining  the 
value  of  this  concentration  have  given  as  an  average 
0.78  Xio~7  at  18°  proves  that  0.0384X10"°  must  be  very 
nearly  the  actual  conductivity  of  absolutely  pure  water, 
A  number  of  other  pure  substances  behave  in  a  similar 
way  at  ordinary  temperatures.  They  have  a  very  low 
conductivity  and  consequently  can  contain  very  few  ions. 
For  instance,  pure  anhydrous  sulphuric  acid  is  very 
weakly  dissociated  according  to  the  scheme 


when  the  two  pure  substances  H2O  and  H2SO4  are 
mixed;  i.e.,  if  H2SO4  is  dissolved  in  water,  the  resulting 
solution  conducts  more  or  less  readily. 

According  to  the  views  developed  in  the  preceding  pages, 
the  reason  for  this  is  that  the  pure  substances  alone  contain 
very  few  ions,  but  mixing  or  dissolving  the  two  sub- 
stances in  some  way  gives  rise  to  the  formation  of  a  large 
number  of  ions. 

An  instructive  example  of  this  general  fact  is  furnished 
by  the  conductivity  of  sulphuric  acid  of  different  strengths. 
The  accompanying  curve  (Fig.  7)  shows  the  relation 
between  the  concentration  and  conductivity  of  H2SO4, 
conductivity  being  plotted  on  the  vertical  axis  and  con- 
centration on  the  horizontal. 

At  the  concentration  zero,  i.e.,  in  pure  water,  the  con- 
ductivity is  practically  zero.  As  the  concentration  of 
H2SO4  increases,  the  conductivity  increases  rapidly  and  at 
32%  reaches  a  maximum.  It  then  falls  off  until  at  82% 
a  minimum  is  reached,  the  solution  at  this  point  having 
a  composition  corresponding  to  the  formula  H2SO4-H2O. 


§2  ELECTROCHEMISTRY. 

This  monohydrate  is  to  be  considered  as  a  comparatively 
poor  conductor.  When  more  sulphuric  acid  is  added  the 
curve  rises  again  (the  following  solutions  may  be  considered 
as  a  solution  of  H2SO4  in  the  hydrate,  H2SO4-H2O),  at 
92%  reaches  a  maximum  and  then  falls  off  practically 
to  o  at  100%.  If  SO3  is  added  to  the  anhydrous  H2SO4  a 


10      .20       30       40       50       60       70       80       90      100  £ 

FIG.  7. 

new  curve  with  another  maximum  is  obtained,  as  shown 
in  the  figure  above  100%. 

Solutions  of  all  other  conducting  substances  behave  in  a 
similar  way,  although  frequently  the  solubility  is  not 
high  enough  to  allow  the  maximum  conductivity  to  be 
attained,  as  the  curve  for  NaCl  shows  (Fig.  7).  The 
more  soluble  LiCl,  however,  shows  the  maximum. 

The  question  now  arises,  does  a  conducting  solution, 
i.e.,  one  containing  many  ions,  always  result  from  the 
mixture  of  two  different  substances?  This  must  be 
answered  in  the  negative.  The  dissociation  depends 
on  the  nature  of  the  two  components  of  the  solution. 
Water  possesses  the  property  of  forming  with  most  of  the 


CONDUCTIVITY.  93 

acids,  bases,  and  salts  solutions  which  conduct  very  well; 
i.e.,  it  compels  the  dissociation  of  these  substances.  We 
say  that  water  has  a  great  "dissociating  powrer";  but 
all  substances  dissolved  in  it  are  not  necessarily  dis- 
sociated. For  instance,  sugar,  urea,  boric  acid,  and 
many  organic  substances  when  dissolved  in  water  give 
non-conducting  solutions,  which  therefore  contain  no 
ions. 

Another  class  of  substances,  the  alcohols,  are  good 
solvents,  though  by  no  means  as  good  as  water;  their 
solvent  power  decreases  with  an  increase  in  molecular 
weight.  Liquid  ammonia  is  almost  as  good  a  solvent  as 
water;  it  dissolves  many  substances  and  gives  solutions 
which  conduct  very  well. 

In  order  to  compare  solvents  with  respect  to  their 
dissociating  power  two  points  must  be  kept  in  mind. 
The  conductivity  of  a  solution  is  dependent  not  only  on  the 
degree  of  dissociation  of  the  dissolved  electrolyte  but  also 
on  the  resistance  or  friction  which  the  ions  must  overcome 
in  moving  through  the  solution.  A  solvent  of  low  disso- 
ciating power  may  give  a  solution  of  higher  conductivity 
than  a  second  solvent  whose  dissociating  power  is  greater. 
If  the  friction  which  the  ions  have  to  overcome  in  one 
solution  is  low  enough,  this  may  more  than  compensate 
for  the  larger  number  of  ions  in  the  other  solution.  Water 
and  liquid  ammonia  are  two  such  solvents:  the  first 
possesses  the  higher  dissociating  power,  but  the  latter 
presents  much  less  resistance  to  the  movements  of  the 
ions,  as  might  be  expected  from  the  mobility  and  volatil- 
ity of  liquid  ammonia. 

Nernst  has  proposed  the  following  explanation  of  the 
ability  of  different  solvents  to  dissociate  dissolved  salts 


94 


ELECTROCHEMISTRY, 


into  the  ions.  The  electrostatic  attraction  of  the  oppositely 
charged  ions  must  evidently  tend  to  diminish  the  dissocia- 
tion of  a  given  salt,  and  acts  in  opposition  to  that  force 
which  strives  to  dissociate  the  compound,  and  whose 
nature  is  as  yet  entirely  unknown.  The  rivalry  between 
these  two  opposing  forces  regulates  the  actual  equilibrium 
of  dissociation.  The  dissociation  must  therefore  increase 
if  the  electrostatic  attraction  is  diminished.  The  study 
of  static  electricity  has  shown  that  two  bodies  having 
opposite  charges  of  electricity  attract  each  other  with 
a  force  which  varies  inversely  with  the  dielectric  constant 
of  the  medium  which  surrounds  the  bodies.  According 
to  this  view  those  solvents  which  have  the  highest  dielectric 
constant  must  have  the  highest  dissociating  power.  This 
rule,  which  was  proposed  simultaneously  by  Thomson  and 
Nernst,  holds  very  well  in  most  cases,  as  is  shown  by  the 
following  table  of  Nernst.* 


Medium 

Dielectric 
Constant 

Electrolytic  Dissociation 

Gases  

I  .0 

Immeasurable  at  ordinary  temperature 

Benzol  

2-3 

Conductivity   extremely   low, 
very  slight  dissociation 

indicating 

Ether        

4.1 

Perceptible     conductivity     of 
electrolytes 

dissolved 

Alcohol        

2S 

Moderate  dissociation 

Formic  acid  

62 

Strong  dissociation 

Water         

80 

Very  strong  dissociation 

*  The  values  of  the  different  dielectric  constants  and  a  table  showing 
the  relation  between  the  dissociating  power  and  a  number  of  the 
physical  properties  of  the  different  solvents  will  be  given  in  Book  II. 


CONDUCTIVITY.  95 

Apparently  most  of  the  physical  properties  of  solvents, 
such  as  "  association,"  dissociating  power,  etc.,  are  in 
some  way  connected.  Dutoit  and  Aston  have  found  that 
solvents  with  a  high  dissociating  power  are  in  general 
inclined  to  polymerization  in  the  liquid  state.  Polymeri- 
zation is  generally  noticed  in  the  case  of  substances  which 
contain  an  element  of  variable  valence,  such  for  instance 
as  NH3,  which  contains  the  tri-  or  pentavalent  element  N 
or  H2O,  which  contains  the  di-  or  tetravalent  element 
oxygen.  The  occurrence  of  these  elements  in  a  compound 
therefore  would  seem  to  be  connected  with  the  dissociat- 
ing power. 

Aside  from  the  dissociating  power  and  internal  friction 
there  are  other  influences  at  work  concerning  whose 
nature  we  are  completely  in  the  dark.  Formic  acid, 
for  instance,  has  a  dielectric  constant  of  62,  and  accordingly 
should  have  a  high  dissociating  power,  nevertheless  HC1 
dissolved  in  formic  acid  gives  a  practically  non-conducting 
solution,  although  salts  like  NaCl,  KBr,  etc.,  conduct 
very  well  in  formic  acid.  In  this  case  the  hydrochloric 
acid  probably  unites  directly  with  the  formic  acid  and  is 
therefore  unavailable  for  conducting  purposes.  In  gen- 
eral the  dissociation  depends  not  only  on  the  solvent 
but  also  on  the  nature  of  the  dissolved  substance.  The 
tendency  of  the  different  elements  and  'radicals  to  take 
up  an  electric  charge — a  tendency  which  makes  itself 
evident  in  the  electromotive  force  of  the  elements — and  the 
ease  or  difficulty  with  which  they  may  be  deposited  on  an 
electrode,  plays  an  important  part  in  determining  the 
relative  dissociation.  The  tendency  of  elements  to  pass 
into  the  ionic  condition  is  closely  related  to  the  general 
chemical  properties  of  the  elements,  and  thus  the  degree 


96 


ELECTROCHEMISTR  Y. 


of  dissociation  becomes  an  important  factor  in  determining 
the  chemical  activity  of  a  dissolved  substance.  We  must 
therefore  consider  the  relations  of  dissociation  somewhat 
more  fully. 

As  we  have  seen  on  p.  87,  the  degree  of  dissociation  is 

calculated  according  to  the  equation  a.  =  —f.    The  folio w- 

^o 

ing  table  shows  how  the  degree  of  dissociation  of  certain 
typical  electrolytes  when  dissolved  in  H2O  changes  with 
the  concentration. 


C=  l/V 

o 

w 

O 
M 

o 
M 

« 

§ 

o 
& 

HN 

o 
% 

W 

HM 

1 

S3 
HH 

HOOD£HO 

» 

O 

ED 
£ 

O.OOOI 

— 

— 

0.99?* 

0.990 

0.992 

0.992 

0.989 

0.308 

0.28 

O.OOI 

0.992 

0.998 

0.979 

°-973 

0.962 

o-959 

0.890 

0.118 

o.  119 

O.OI 

0.974 

°-973 

0.941 

0-931* 

0.886 

0.873 

0.664 

0.041 

0.041 

O.  I 

0.924 

0.860 

0.861 

0.830 

o-759 

0.713 

0.418 

0.013 

0.014 

I 

0.792 

0.786 

°-755 

0.628 

o-579 

o-534 

0.241 

— 

— 

The  first  vertical  column  contains  the  concentration 
c  (reciprocal  of  the  dilution),  the  others  contain  the 
degree  of  dissociation  of  the  different  substances  at  these 
particular  concentrations.  HC1  is  dissociated  the  most, 
and  the  dissociation  of  the  other  strong  monobasic  acids 
as  HNO3,  HC1O,  HBr,  HI,  etc.,  follows  that  of  HC1 
closely;  the  bases  NaOH.  KOH,  LiOH,  T1OH,  etc.,  are 
also  just  as  highly  dissociated.  The  i :  i  salts  are  slightly 
less  dissociated;  still  less  the  1:2  salts,  while  the  2:2 
salts  like  ZnSO4  are  the  least  dissociated.* 

*  By  a  i :  i  salt  is  meant  one  derived  from  a  monobasic  acid  and  a 


CONDUCTIVITY.  97 

The  strength  of  the  acid  and  base  from  which  the  salt 
is  derived  has  considerable  influence  on  the  degree  of 
dissociation.  The  K  salt  of  the  weak  acetic  acid  is  less 
dissociated  than  the  corresponding  salt  of  the  stronger 
hydrochloric  acid.  This  fact  is  still  more  evident  when  we 
compare  the  acids  and  bases  themselves,  for  instance, 
acetic  with  hydrochloric  acid:  ammonia  with  potassium 
hydroxide;  etc.  Since  the  H*  ion  is  common  to  all  acids 
and  always  has  the  same  tendency  to  take  up  an  electric 
charge  the  difference  in  the  degrees  of  dissociation  can 
only  be  due  to  the  fact  that  chlorine  has  a  much  higher 
tendency  to  pass  into  the  ionic  condition  than  the  acetic- 
acid  radical,  i.e.,  it  has  a  higher  "  electro-affinity." 

Strength  of  Acids  and  Bases. 

The  degree  of  dissociation  is  of  the  highest  importance 
in  determining  the  chemical  activity  of  an  acid  or  base. 
The  common  characteristic  of  all  acids  is  the  formation 
of  H*  ions  in  a  water  solution,  consequently  in  all  re- 
actions which  may  be  brought  about  by  any  acid  and 
which  therefore  depend  on  the  presence  of  the  H*  ion,  the 
concentration  of  the  H*  ion  is  of  decisive  importance.  In 
a  similar  way  the  common  property  of  all  bases  is  their 
ability  to  form  OH'  ions  in  a  water  solution,  consequently 
the  bases  will  act  more  vigorously  according  as  their  degree 
of  dissociation  is  high  or  low. 

The  strength  of  a  base  or  acid  makes  itself  felt  in  the 
reaction  of  distribution.  If  we  add  to  a  solution  of  NH3 

monacid  base;  1:2  are  derived  from  a  monobasic  acid  and  diacid  base, 
or  vice  versa,  as  BaCl2,  or  Na2SO4,  etc.  2:2  are  such  as  ZnSO4, 
MgCO3,  etc. 


98  ELECTROCHEMISTRY. 

and  KOH  an  amount  of  HC1  which  is  less  than  sufficient 
to  neutralize  both  bases,  this  acid  will  be  distributed 
between  the  .two  bases.  Both  potassium  and  ammonium 
chloride  will  be  formed,  but  more  of  that  salt  whose  base  is 
the  stronger.  In  the  same  way  a  base  is  distributed 
between  two  acids,  so  that  the  larger  part  falls  to  the  lot 
of  the  stronger  acid.  Further,  if  we  add  to  the  salt  of  a 
weak  base,  such  as  NKUCl,  the  stronger  base  KOH,  a 
redistribution  of  the  HC1  takes  place,  the  KOH  takes 
the  acid  from  the  ammonia,  the  latter  is  set  free  and  may 
be  driven  out  of  the  solution  by  boiling.  Still  further, 
if  we  add  hydrochloric  acid  to  a  solution  of  sodium  acetate 
the  HC1  displaces  the  acetic  acid.  In  all  these  cases, 
however,  the  displacement  takes  place  only  till  a  state  of 
equilibrium  is  reached,  and  this  equilibrium  is  determined 
by  the  value  of  the  dissociation  constants  of  the  acids  and 
bases.*  It  has  been  found  that  the  ratio  of  distribution  is 
equal  to  the  ratio  of  dissociation  of  the  two  acids  or  bases 
at  the  dilution  in  question. 

The  strength  of  an  acid  also  makes  itself  felt  in  a 
certain  class  of  reactions  which  are  "  catalytically  "  ac- 
celerated by  the  presence  of  H*  ions.  Such  a  reaction 
is  the  inversion  of  cane-sugar  into  levulose  and  dextrose, 
which  causes  a  good  deal  of  trouble  in  the  refining  of 
sugar,  since  the  two  resulting  compounds  are  very  hard 
to  crystallize.  The  reaction 


proceeds  very  slowly  in  a  neutral  solution,  but  is  greatly 
accelerated   by   the   presence   of   acids.     This   catalytic 

*  For  the  relation  between  the  dissociation  constant  and  the  distri- 
bution, cf.  Nernst,  Theoretische  Chemie,  1903,  p.  506. 


CONDUCTIVITY  99 

acceleration  is  greater  according  to  the  number  of  H*  ions 
which  a  given  acid  can  supply;  in  other  words,  the  acid 
accelerates  this  reaction  more  or  less  according  as  it  is( 
strongly  or  weakly  dissociated.  If  the  acids  are  arranged 
in  the  order  of  their  conductivity  this  same  order  represents 
also  their  relative  activity  in  accelerating  the  inversion 
of  sugar.  A  similar  case  is  furnished  in  the  decomposition 
of  the  ester: 

CHaCOOCsH,,  +±  CH3COOH  +  C5Hlo. 

This  reaction  is  accelerated  to  a  different  degree  by 
strongly  and  weakly  dissociated  acids. 

The  strength  of  a  base  regulates  the  velocity  of  the 
reaction  of  saponification.  The  higher  the  dissociation 
of  a  base  the  faster  it  will  saponify  the  ethereal  salts  of  the 
fatty  acids. 

As  yet  we  have  considered  the  connection  between  the 
dissociation  and  strength  of  an  acid  or  base  only  in  a 
qualitative  way.  How  can  we  obtain  definite  quantitative 
relations  ? 

The  law  of  mass  action  applies  to  the  reaction  of  disso- 
ciation, as  it  does  to  all  reactions.  If  we  write  the  equation 
for  the  dissociation  of  acetic  acid, 

CH3COOH  ?=*  CH3COO+H', 
and  apply  to  this  the  mass-action  law  we  have 


ca  represents  the  concentration  of  the  undissociated 
molecules  and  Ci  that  of  the  ions.  (In  any  solution  the 
concentration  of  the  two  different  kinds  of  ions  must 


100 


ELECTROCHEMISTR  Y. 


necessarily  be  equal.)  K  is  the  dissociation  constant.  If 
the  value  of  K  is  known  for  any  acid  or  base  the  value  of 
the  dissociation  may  be  at  once  calculated  for  any  dilution, 
and  also  the  conductivity,  if  the  values  of  /0'  and  /0'  are 
known,  van't  Hoff  and  Reiche  give  the  following  table 
for  acetic  acid: 

MOLECULAR  CONDUCTIVITY  OF  ACETIC  ACID  AT  14.1°. 


V 

Av 

iooa 
Observed 

rooa 
Calculated 

0.994 

1.27 

0.402 

0.42 

2.02 

1.94 

0.614 

0.6o 

15-9 

5-26 

1.66 

1.67 

18.9 

5.63 

I.78 

I.78 

K=  0.0000178 

1500 

46.6 

14.7 

JS-0 

log  #=5.25-10 

3010 

64.8 

20.5 

20.2 

4)=  316 

7480 

95-i 

3O.I 

30.5 

15000 

129 

40.8 

40.  I 

[«° 

316 

100 

100] 

The  first  column  contains  the  dilution  in  litres  per  mol, 
the  second  the  observed  molecular  conductivities  Av ,  the 
third  the  value  of  a  calculated  from  the  conductivity 

measurements  by  means  of  the  formula  cc  =  -~.      In  the 

^o 

fourth  column  are  the  values  of  a  calculated  from  the 
equation  Kv(i  —  a)=a2,  using  0.0000178  as  the  value  of 
K.  The  equation  cs  =  Kci2  is  identical  with  this  since 

c8  =  —  -  and  c\=— .  In  regard  to  the  physical  signifi- 
cance of  K  the  following  may  be  said:  in  the  case  of  a 
binary  electrolyte  (i.e.,  one  which  dissociates  into  two 
ions)  K  is  equal  to  half  the  concentration  at  which  the 
electrolyte  is  50%  dissociated.* 


*  This  is  readily  shown  by  substituting  0.5  for  a  in  the  equation. 


CONDUCTIVITY.  101 

Strange  to  say,  this  law,  which  was  first  derived  by 
Ostwald  and  is  known  as  the  Ostwald  dilution  law,  holds 
only  for  electrolytes  which  are  weakly  dissociated.  It 
does  not  at  all  fit  the  case  of  highly  dissociated  salts.  A 
possible  reason  for  this  is  the  following:  in  calculating 
the  dissociation  we  tacitly  assumed  that  the  mobilities 
of  the  ions  V  and  /</  were  independent  of  the  concentration, 
and  that  the  friction  they  meet  with  on  the  part  of  the 
solvent  is  not  affected  by  the  presence  of  the  undissociated 
molecules  and  other  ions.  Since  Ostwald's  law  holds 
for  weak  electrolytes  where  a  great  many  undissociated 
molecules  are  present,  it  has  been  argued  that  these  must 
be  without  effect  on  the  velocity  of  the  ions.  In  the  case 
of  the  strongly  dissociated  salts  where  very  many  ions  are 
present  some  disturbing  factor  is  present,  and  it  seems  as 
if  the  ions  have  some  mutual  influence  on  each  other's 
velocity.  Still  it  is  quite  possible  that  the  undissociated 
molecules  have  a  favorable  effect  on  the  mobility  of  the 
ions;  with  a  slightly  dissociated  electrolyte,  where  the 
relative  number  of  undissociated  molecules  is  only 
slightly  increased  as  the  concentration  increases,  this 
may  have  an  unnoticeable  effect  on  the  value  of  K,  but 
with  a  strong  electrolyte  the  effect  may  be  very  great. 
The  whole  matter  has  not  yet  been  satisfactorily  cleared 
up. 

From  the  law  of  mass  action  the  following  rule  has  been 
derived :  For  a  binary  electrolyte  the  ionic  concentration 
and  consequently  the  conductivity,  is  proportional  to  the 
square  root  of  the  total  concentration  when  the  electrolyte 
is  not  very  strongly  dissociated. 

For  highly  dissociated  electrolytes  van't  Hoff  has  found 
empirically  that  the  following  expression  holds  true: 


102  ELECTROCHEMISTRY 

-^2  =  a  constant, 

Cs 

and  from  this  the  conductivity  may  be  calculated.  Ac- 
cording to  this  the  cube  of  the  concentration  of  the  ions  is 
proportional  to  the  square  of  the  concentration  of  the 
undissociated  molecules. 

The  dissociation  constants  of  different  electrolytes 
may  have  widely  differing  values,  as  the  following  table 
of  "  affinities  "  of  a  number  of  acids  aixd  bases  shows: 

K 

Acetic  acid,  CH3COOH o .  0000180 

Mono-chlor-acetic  acid,  CH2C1COOH 0.00155 

Tri-chlor-acetic  acid,  CC13COOH 1.21 

Ammonia,  NH4OH o .  000023 

Methylamine,  NH3CH3OH o .  00050 

Aniline,  NH3C.HSOH i .  iX  io-10 

Carbonic  acid,  HCO3H 3Q4oX  io~10 

Hydrogen  sulphide,  HSH 57oX  io~10 

Boric  acid,  H3BO3 iyX  io-10 

Prussic  acid,  CNH i3X  io-10 

Phenol,  CGH5OH i  .3X  io-10 

One  very  important  consequence  of  the  law  of  mass 
action  is  the  following:  the  dissociation  of  acetic  acid 
follows  the  equation 

CH3COOH  ^  CH3COO'  +  H\ 
The  law  of  mass  action  requires 


If  an  excess  of  either  of  the  ions  is  introduced  into  the 
solution  of  acetic  acid,  for  instance  CH3COO',  by  the 

*  The   concentration   of   any   compound   or   radical   is   indicated   by 
enclosing  the  symbol  in  brackets. 


CONDUCTIVITY.  103 

addition  of  CH3COONa  or  H*  by  addition  of  a  strong 
acid,  the  equilibrium  is  disturbed.  The  right-hand  side 
of  the  equation  becomes  too  large  and  in  order  for  K  to 
remain  constant  the  dissociation  must  decrease. 

If  two  solutions  have  a  common  ion  and  their  concen- 
tration with  respect  to  this  ion  are  the  same,  then  their 
solutions  may  be  mixed  and  no  change  in  the  state  of 
dissociation  of  either  of  the  substances  will  occur;  such 
solutions  are  called  "  isohydric." 

Two  solutions  of  acids  whose  dissociation  follows  the 
law  of  mass  action — for  instance  acetic  and  propionic 
acids — are  without  effect  on  their  mutual  dissociation,  i.e., 
are  isohydric  when  their  concentrations  stand  in  the 
inverse  ratio  of  their  dissociation  constants. 

This  forcing  back  of  the  dissociation  by  the  addition 
of  a  solution  containing  a  common  ion  is  of  great  im- 
portance in  many  analytical  operations.  The  theory 
of  dissociation  has  explained  the  mode  of  action  of 
many  empirical  chemical  receipts.  For  instance,  the 
dissociation  of  a  normal  solution  of  acetic  acid  is  0.4%, 
but  this  is  reduced  to  0.0018%  if  a  gram  equivalent  of 
sodium  acetate  is  added  to  the  solution.  Since  the 
strength  of  the  acid,  or  the  intensity  with  which  it  takes 
part  in  reactions  or  accelerates  them  (cf.  the  inversion 
of  sugar,  p.  98)  is  determined  by  the  concentration  of  the 
H*  ions,  it  is  evident  that  acetic  acid  is  very  much  weakened 
by  the  addition  of  CH3COONa.  The  same  is  true  of 
other  acids  and  bases.  For  instance,  the  precipitation 
of  ZnS  by  H^S  is  prevented  by  the  addition  of  acid,  for 
the  H*  ions  of  the  acid  cause  a  great  decrease  in  the 
dissociation  of  the  H2S  with  a  consequent  decrease  in  the 
number  of  S"  ions.  For  the  same  reasons  the  precipita- 


104  ELECTROCHEMISTRY. 

tion  of  Mg(OH)2  by  NH4OH  is  prevented  by  the  previous 
addition  of  ammonium  salts.  The  forcing  back  of  the 
dissociation  is  also  of  great  importance  in  all  reactions  of 
precipitation.  If  we  wish  to  precipitate  Ag*  ions  by  Cl' 
ions  and  add  an  amount  of  chlorine  which  is  exactly 
equivalent  to  the  silver,  then  a  quantity  of  silver  corre- 
sponding to  the  solubility  of  AgCl  remains  in  solution. 
This  is  o.ooooi  i  mol.,  i.e.,  a  saturated  solution  of  AgCl 
contains  o.ooooi  i  X  ro8  =  i.  2  mgr.  of  silver.  In  washing  a 
silver-chloride  precipitate  an  appreciable  error  might  be 
introduced  owing  to  the  solubility  of  the  precipitate. 
The  law  of  mass  action  requires  for  the  reaction  of  solution 

#[AgClsolid]  =  [AgCldissoived]  =  o.ooooi  i  . 

In  this  very  dilute  solution  we  may  assume  that  the  disso- 
ciation is  practically  complete,  so  that 


Then 


L  is  the  "  solubility  product  "  of  silver  chloride.  If  we 
add  KC1  so  that  the  solution  is  normal  with  respect  to 
the  chlorine  ions,  then,  since  L  is  a  constant,  the  con- 
centration of  the  silver  ions  will  be  reduced  to  1.2  Xio~10, 
a  value  too  small  to  be  of  any  analytical  importance.  It 
is  customary  therefore  to  add  an  excess  of  KC1  for  the 
precipitation,  and  to  wash  with  a  solution  containing 
Cl'  ions,  as  dilute  HC1.  For  similar  reasons  a  number 
of  sulphide  precipitates  are  washed  with  water  contain- 
.ing  H2S. 

These  facts  may  easily  be  demonstrated  in  the  case  of 
PbCi2.     If  a  few  drops    of  a  strong    solution  of  NaCI 


CONDUCTIVITY.  105 

are  added  to  a  saturated  solution  of  PbCl2,  a  heavy  white 
precipitate  forms;  the  dissociation  is  forced  back  by  the 
addition  of  the  chlorine  ions  and  more  undissociated 
PbCl2  results  than  corresponds  to  the  solubility,  and  this 
excess  appears  as  a  precipitate. 

The  examples  cited  above  of  the  precipitation  of 
Mg(OH)2  by  ammonia  and  of  ZnS  by  H2S  depend  on  the 
reverse  process.  The  addition  of  an  ammonium  salt  to  the 
ammoniacal  magnesium  salt  solution  robs  the  NH4OH 
of  a  large  share  of  its  basic  nature;  OH'  ions  and  NH4* 
ions  can  only  exist  in  a  solution  in  such  amounts  as  are 
governed  by  the  dissociation  constant  of  NH4OH.  On 
adding  NH4'  ions  in  the  form  of  a  salt,  the  concentration 
of  the  OH'  ions  is  greatly  reduced,  and  consequently  in 
the  mass  action  equation 


the  right-hand  side  becomes  too  small,  and  therefore 
much  more  Mg"  will  go  into  solution  than  if  no  NH4  salt 
were  present. 

The  quantitative  relations  may  be  obtained  when  we 
consider  the  matter  as  a  question  of  distribution  (p.  97). 
When  a  strong  base  such  as  NaOH  is  added  to  a  Mg 
salt,  the  anion  of  the  Mg  salt  is  distributed  between  both 
the  Na  and  the  weaker  Mg,  consequently  a  large  amount 
of  Mg(OH)2  is  formed  and  appears  as  a  precipitate. 
The  NH4OH,  however,  which  has  been  weakened  by  the 
addition  of  NH4  salt,  is  no  longer  able  to  displace  the 
Mg  from  its  salts. 

As  yet  we  have  considered  only  such  dissociations  as 
take  place  according  to  one  equation.  But  with  many 
salts  two  stages  in  the  dissociation  are  possible.  The 


106  ELECTROCHEMISTRY. 

most  important  example  is  water,  which  dissociates  ac- 
cording to  the  two  equations 


(i) 
and 

(2)     H20<=±H'+H- 

The  second  dissociation,  however,  takes  place  to  a  very 
slight  extent,  or,  as  we  may  also  put  it,  the  dissociation 
constant  of  the  second  H"  ion  is  very  much  smaller  than 
that  of  the  first.  Similar  reactions  are  possible  with 
many  other  substances,  for  instance 

(i) 
(2) 
(i)  BaCl2<=±BaCl- 

(2) 

It  sometimes  happens  that  two  molecules  unite  and 
then  dissociate  by  "  steps."  With  CdCl2  the  following 
modes  of  dissociation  are  possible  : 


2CdCl2  <=>  Cd2Cl2"  +  Cl'  +  Cl' 


3',  etc. 

This  polymerization  of  the  molecules   is   the  cause  of 
many  of  the  deviations  from  the  laws  of  solutions. 


CONDUCTIVITY.  107 

Conductivity  and  Temperature. 

The  temperature  has  a  great  effect  on  the  conductivity 
of  the  electrolytes,  and  the  temperature  coefficient  is 
practically  always  positive,  i.e.,  the  conductivity  increases 
as  the  temperature  rises.  Two  causes  must  be  dis- 
tinguished. ,  The  dissociation  of  most  salts  decreases  as 
the  temperature  rises,  and  this  decrease  though  generally 
small  should  lower  the  conductivity.  On  the  other  hand, 
the  mobility  of  the  ions  is  much  increased  and  this  tends 
to  increase  the  conductivity. 

The  temperature  coefficient  of  most  salts  hi  water  has 
such  a  value  that  at  about  —30°  the  conductivity  would 
be  zero.  Since  the  fluidity  of  water  (reciprocal  of  the 
internal  friction)  follows  a  temperature  formula  which 
also  gives  zero  as  the  value  for  —  30°,  it  seems  clear  that 
the  influence  of  temperature  on  the  conductivity  is  due 
to  the  effect  of  the  temperature  on  the  internal  friction 
of  water. 

At  ordinary  temperatures  the  temperature  coefficient  of 
dilute  solutions  of  salts  is  from  0.02  to  0.023,  i-e-> tne  con" 
ductivity  is  raised  by  2  —2.3%  for  i  degree  rise  in  tempera- 
ture. For  acids  and  some  acid  salts  the  coefficient  is 
0.009  to  0.016,  for  alkalies  it  is  0.019  to  0.02. 

The  temperature  coefficient  depends  but  little  on  the 
concentration.  In  nearly  all  cases  it  decreases  slightly 
as  the  concentration  rises,  and  then  rises  again  at  higher 
concentrations.  With  certain  salts  such  as  the  chlorides 
and  nitrates  of  K  and  NH4  the  decrease  persists  even  in 
the  stronger  solutions.* 

*  A  classic  work  on  the  conductivity  of  the  electrolytes  is  the  book 
by  Kohlrausch  and  Holborn,  published  by  Teubner  of  Leipzig,  which 


Io8  ELECTROCHEMISTRY. 

The  high  temperature  coefficient  of  substances  which 
conduct  electrolytically  is  of  especial  importance  in  the 
case  of  solid  salts.  At  ordinary  temperatures  these  are 
practically  non-conductors,  but  at  higher  temperatures 
the  conductivity  increases  greatly,  and  salts  in  a  state  of 
fusion  are  among  the  best  conductors.  Even  solid 
substances  when  highly  heated  may  show  considerable 
conducting  power.  A  good  example  is  furnished  by  the 
"  glower  "  of  the  Nernst  light. 

The  Transport  Number. 

We  will  consider  first  a  binary  electrolyte,  say  NaCl. 
If  we  send  a  unit  quantity  of  electricity  through  this 
solution  both  ions  take  part  in  transporting  the  current? 
and  since  the  concentrations  of  the  two  ions  are  equal  and 
the  pull  exerted  by  the  electrodes  is  the  same  for  both,  the 
part  taken  by  each  in  the  conduction  will  be  proportional 
to  the  velocity  of  the  ions.  If  E'  is  the  quantity  of  elec- 
tricity transported  by  the  anion  and  E'  the  part  transported 
by  the  cation,  then 

E'+E'  =  E    and    E':E'  =  V:U, 

where  U  and  V  are  the  velocities  of  the  cation  and  anion 
respectively.     We  then  obtain 

E':E=V:U+V     and     E':E=U:U+V. 

The  phenomena  attending  the  passage  of  the  current 
will  be  better  understood  from  Fig.  8.  A  tube  which 
is  divided  into  three  compartments  by  two  porous  dia- 
phragms contains  at  one  end  the  anode  and  at  the  other 

contains   the   theory  of   the  methods   of  measurement   and  extended 
tables. 


CONDUCTIVITY. 


109 


the  cathode.  At  first  the  electrolyte  has  the  same  con- 
centration throughout  the  tube  as  is  indicated  by  the 
upper  series  of  ±  signs.  Every  ±  sign  represents  a  gram- 
molecule  of  salt,  the  +  signs  represent  the  cations,  and  the 
—  signs  the  anions.  Let  us  assume  that  the  velocity  of  the 
cation  is  to  that  of  the  anion  as  5:3.  We  send  16  F* 
through  the  solution,  which  results  in  the  separation  of 


Before 


Anode 


Diaphragms 

FIG.  8. 


Cathode 


1 6  mols  of  cations  at  the  cathode  and  16  mols  of  anions 
at  the  anode. 

In  the  actual  transporting  of  the  current  the  ions  take 
part  in  the  ratio  of  their  velocities,  i.e., 

E-:E'  =  icF:  6F 
E".E  =  ioF:i6F 
E':E  =  6F:i6F. 

While  the  +  ions  all  move  5  units  of  length  in  one  direc- 
tion the  —  ions  move  3  units  in  the  other.  The  final 
distribution  is  shown  by  the  lower  series  of  ±  signs  of 
Fig.  8.  It  is  seen  that  16  mols  have  been  set  free  at  each 
electrode,  the  concentration  in  the  middle  compartment 

*  In  honor  of  Faraday  the  charge  on  i  gr.  equivalent  of  ions  or  96  540 
coulombs  is  represented  by  F. 


i 1 o  ELECTROCHEM1S TR  Y. 

remaining  unchanged,  while  that  in  each  electrode  com- 
partment has  changed  to  a  different  degree.  The  changes 
in  the  salt  concentration  in  each  of  the  electrode  com- 
partments are  to  each  other  as  the  velocities  of  the  ions 
which  have  left  those  compartments.  In  this  case  the 
change  at  the  cathode  is  to  the  change  at  the  anode  as 
the  velocity  of  the  anion  is  to  the  velocity  of  the  cation  cr 
as  3  is  to  5. 

The  value  of  -^    can  therefore  be  found  by  sending  a 

known  quantity  of  current  through  a  suitable  form  of 
apparatus  and  determining  before  and  after  the  concen- 
trations in  the  electrode  compartments.  The  fact  that 
the  concentration  in  the  middle  compartment  does  not 
change  is  a  proof  that  diffusion  has  not  influenced  the 
result.* 

The  above  method  only  applies  when  the  ions  are 
precipitated  or  otherwise  removed  from  the  solutions.  If 
instead  of  the  ion  which  has  transported  the  current, 
some  other  ion  is  set  free,  it  is  necessary  to  calculate  by 
Faraday's  law  (p.  52)  how  much  of  the  first  ion  should 
have  been  removed  by  the  electrolysis  and  subtract  this 
from  the  concentration  found  before  we  can  tell  how  the 
concentration  has  been  affected  by  the  wandering  of  this 
ion. 

If  the  original  concentration  is  c,  and  the  concentrations 
after  electrolysis  are  c'  at  the  cathode  and  cf  at  the  anode, 
so  that  the  losses  at  the  electrodes  are  c  —  c'  and  c  —  cf 
respectively,  then 

V:U=c-c':c-cf. 

*  For  more  detailed  information  concerning  the  methods  of  measure-* 
Went  and  calculation  of  re^ul^  cf,  5Q9fe  JJ, 


CONDUCTIVITY.  ill 

U:  V  is  the  ratio  between  the  velocities  of  the  two  ions. 
Hittorf  (1856),  who  was  the  first  to  investigate  this  subject, 

V 
called  the  fraction   ,.  ,y==n  the  "transport  number  of 

V  U 

the  anion."     Since  •,,     v  and  rr,v  together  are  equal 

to   one,    •          =i—n  is   the   transport   number  of  the 

cation. 

With  the  help  of  this  new  term  we  may  now  summarize 
the  most  important  formulae  concerning  the  conductivity 
of  an  electrolyte.  If  y  represents  the  concentration  in 
mols  per  c.c.,  a  the  degree  of  dissociation,  then  a y  is 
the  concentratiorrbf  the  ions  and  the  specific  conductivity 
K  is 

K=arjF(U+V). 

Putting  10'  =  FU  and  1Q'  =  FV  (cf.  p.  84),  then 
K=ar)(l0'+I0'). 

Now  the  molecular  conductivity  is  A  =  —  and  we  obtain 

A  =  a(lo'+lo).  At  very  great  dilutions  a  =  i,  conse- 
quently if  we  represent  by  A0  the  molecular  conductivity 

at  extreme  dilutions  then  AQ  =  IQ'+IQ'. 

•  • 

l0'  =  nA0    and    IQ'  =  (I—  n)A0. 

These  last  equations  are  the  mathematical  expression 
of  Kohlrausch's  law  of  the  independent  wandering  of  the 
ions, 


H2  ELECT  ROCHE  MIS  TR  Y. 

Absolute  Velocity  of  the  Ions. 

The  velocities  or  mobilities  /'  and  /'  are  based  on  the 
ohm  as  the  unit  of  resistance  (cf.  p.  79).  In  order  to 
obtain  U  and  F,  the  acutal  velocities  in  centimetres  per 
second  with  which  the  ions  move  in  a  field  where  the  fall 
of  potential  is  i  volt  per  centimetre,  we  must  remember 
that  each  gram  equivalent  of  ions  carries  with  it  96  540 
coulombs,  and  since  the  conductivities  V  and  /</  repre- 
sent velocity  X  charge  we  have 

96  540(17+ F)-/o'+V. 

Accordingly  we  obtain  the  actual  velocities  U  and  V  in 
centimetres  per  second  by  dividing  the  mobilities  /  by 
96  540.  For  infinite  dilution  the  following  are  the  cal- 
culated absolute  velocities  of  some  of  the  ions  at  18°. 


£7  of 

K- 

=  0.000669  cm. 

U  " 

NH4- 

=  0.000667 

<  t 

U  " 

Na- 

=  0.000450 

<  t 

U  " 

Li- 

=  0.000346 

1  1 

U  " 

Ag' 

=  0.000559 

(  i 

U  " 

H- 

=  0.003415 

1  1 

V  " 

CF 

=  0.000667 

(  i 

V  " 

N03' 

=  0.000640 

(  t 

V  n 

C103' 

=  0.000570 

1  1 

V  '< 

OH' 

=  0.001802 

i  i 

It  is  possible  to  calculate  the  force  which  must  be 
exerted  on  an  ion  to  give  it  a  velocity  of  i  centimetre  per 
second.  This  force  is  about  io10,  i.e.,  a  force  represented 
by  the  weight  of  io  ooo  ooo  coo  kilograms.  We  may 


CONDUCTIVITY.  113 

easily  see  that  such  a  force  is  necessary  when  we  remember 
that  a  finely  divided  precipitate  often  requires  many 
hours  to  settle,  on  account  of  the  friction  against  the 
solvent  which  the  particles  must  overcome.  It  is  not 
surprising  therefore  that  the  ions,  which  are  very  many 
times  smaller  than  the  finest  particle  of  a  precipitate, 
meet  with  such  an  enormous  friction.  The  acturl 
velocities  of  the  ions  are  capable  of  direct  measurement  by 
a  method  first  worked  out  by  Whetham  and  Masson, 
and  later  improved  by  Abegg  and  Steele.  The  observed 
and  calculated  results  are  in  perfect  agreement.* 

Dielectric  Constants. 

Two  bodies  carrying  an  opposite  charge  of  electricity 
attract  each  other,  and  the  force  of  this  attraction  varies 
with  the  nature  of  the  medium  surrounding  the  two 
bodies.  If  k  is  the  attraction  when  the  bodies  are  placed 
in  a  vacuum  and  k'  the  attraction  in  some  other  medium, 
then  the  dielectric  constant  DC  of  this  medium  is  given 

k 
by  JDC  =  T>.     For  the  vacuum  DC  =  i  and  is  but  slightly 

greater  than  i  for  the  different  gases.  In  water  the 
attraction  is  -gV  of  that  in  a  vacuum,  i.e.,  the  dielectric 
constant  of  water  is  80. 

The  capacity  of  a  condenser,  i.e.,  the  quantity  of 
electricity  which  it  is  necessary  to  add  in  order  to  give 
the  two  plates  a  difference  of  potential  of  i  volt,  varies 
directly  with  the  dielectric  constant  of  the  medium  which 
occupies  the  space  between  the  two  plates  of  the  condenser. 
If  c  is  the  capacity  when  air  is  used,  the  capacity  is  cDC 

*  For  details  cf.  Book  II. 


1 1 4  ELEC  TROCHE  MIS  TR  Y. 

when  a  substance  whose  dielectric  constant  is  DC  is 
used. 

According  to  the  theory  of  electric  vibrations  the 
velocity  with  which  electric  waves  travel  along  wires  varies 
inversely  as  the  square  root  of  the  dielectric  constant  of 
the  surrounding  medium. 

The  methods  of  measuring  the  dielectric  constant  are 
founded  on  these  two  laws.  The  quantity  of  electricity 
is  measured  which  is  necessary  to  charge  a  given  con- 
denser; this  is  best  done  by  the  use  of  the  Wheatstone 
bridge.  Or  the  deflection  of  the  needle  of  a  quadrant 
electrometer  is  observed  once  in  air  and  again  in  the 
medium  in  question,  and  thus  the  difference  in  the  force 
of  attraction  between  the  needle  and  the  quadrants  is 
directly  determined  for  the  two  media.  Another  method, 
worked  out  by  Drude,  depends  on  the  determination  of 
the  length  of  electric  waves  along  wires  surrounded  by 
different  media.  A  table  of  the  values  of  the  dielectric 
constants  of  a  number  of  substances  which  can  be  used  as 
solvents  for  electrolytes  will  be  given  in  Book  II,  and  also 
a  more  complete  description  of  the  methods  of  measure- 
ment. 


CHAPTER  V. 


ELECTROMOTIVE  FORCE  AND  THE  GALVANIC 
CURRENT. 

To  aid  in  forming  a  clear  idea  of  the  relations  between 
current  and  voltage  we  will  make  use  of  an  illustration, 
although  this  illustration,  like 
all  comparisons,  does  not  hold 
at  all  points.  Suppose  we 
have  an  air-tight  ring-shaped 
tube  filled  with  air.  At  a 
point  A  in  Fig.  9  we  place  a 
pumping  arrangement  which 
draws  in  air  on  one  side  and 
expels  it  on  the  other.  As  a 
result  a  partial  vacuum  is 
created  to  the  right  of  the 
pump  and  the  pressure  of 
the  air  on  the  other  side  is 
raised.  The  air  seeks  to 
equalize  this  difference  in 
pressure  by  flowing  around 
through  the  tube  from  left  to 
right,  and  the  pump  strives  to  keep  up  the  difference  in 
pressure.  As  a  result  a  stationary  condition  is  arrived 

"5 


FIG.  9. 


n6  ELECTROCHEMISTRY. 

at  when  the  quantity  of  air  flowing  around  through  the 
tube  from  left  to  right  is  the  same  as  that  brought  over 
by  the  pump-  from  right  to  left.  From  right  to  left  along 
the  tube  the  difference  in  pressure  gradually  falls  off, 
as  is  indicated  in  the  figure  by  the  different  lengths  of 
the  arrows.  In  the  narrow  part  of  the  tube  where  the 
air  finds  the  greatest  resistance  the  pressure  falls  off  most 
rapidly.  If  the  tube  is  closed  at  any  point  the  pump 
continues  working  for  a  short  time  and  forces  air  over 
till  the  difference  in  pressure  between  the  ends  of  the  tube 
is  the  same  as  the  pressure  which  the  pump  can  exert. 

Let  us  now  take,  in  place  of  the  tube,  a  wire  through 
which  electricity  can  flow,  and  replace  the  air-pump  by 
an  electricity  pump  which  takes  in  positive  electricity  on 
one  side  and  gives  it  out  on  the  other  (or  what  amounts 
to  the  same  thing,  gives  out  positive  electricity  on  one  side 
and  negative  on  the  other).  For  this  purpose  we  may  use 
a  battery  or  a  dynamo.  In  the  first  illustration  the  air 
pressure  on  the  left  was  raised  and  on  the  right  lowered; 
in  this  case  also  the  electric  pressure,  or  "  potential,"  is 
raised  on  the  left  and  lowered  on  the  right. 

The  electricity  seeks  to  equalize  this  difference  of 
potential  by  flowing  around  through  the  wire,  while  the 
battery  strives  to  maintain  the  constant  difference  of 
potential.  The  potential  falls  off  along  the  wire  from 
the  left  pole  around  to  the  right,  and  it  decreases  most 
rapidly  at  those  points  where  the  electricity  finds  the 
greatest  friction,  i.e.,  where  the  resistance  of  the  circuit 
is  highest.  If  we  cut  the  wire  at  any  point  so  that  elec- 
tricity can  no  longer  flow,  the  battery  still  continues  to 
work  for  an  instant,  but  only  until  the  difference  of 
potential  between  the  ends  of  the  wire  is  the  same  as  the 


ELECTROMOTIVE  FORCE  AND   GALVANIC  CURRENT, 


electromotive  force  of  the  battery.  The  amount  of 
electricity  which  is  necessary  to  bring  the  ends  of  the  wire 
up  to  this  potential  is  known  as  the  capacity  of  the  wire; 
the  capacity  is  equal  to  one,  when  i  coulomb  is  required  to 
give  a  difference  of  potential  of  i  volt. 

If  the  circuit  is  closed  so  that  a  current  can  pass,  Ohm's 
law  applies  to  every  portion  of  the  circuit  (cf.  p.  78).  If 
s  is  the  difference  of  potential 
between  any  two  points,  w  the 
resistance,  and  i  the  quantity  of 
electricity  passing  per  second, 
then  e  =  iw.  If,  in  Fig.  10,  P« 
and  P_e  represent  the  poten- 
tials on  the  left-  and  right-hand 
sides  of  the  battery  when  the 
circuit  is  open,  so  that  P£-P_  e 
represents  the  electromotive 
force  of  the  battery,  then  the 
potential  will  gradually  fall  off 
along  the  wire  from  Pe  to  P_£ 

when  the  circuit  is  closed.  Let  the  potential  at  different 
points  along  the  wire  be 


FIG.  10. 


and  let  the  value  of  each  be  indicated  'by  the  length  of 
the  arrow.  PQ  represents  the  original  potential  of 
the  wire  before  the  battery  was  attached  and  the  direc- 
tion of  the  arrows  shows  whether  the  potential  at  any 
point  is  higher(  \  )  or  lower  (  j  )  than  at  P0. 

If  the  electromotive  force  at  the  terminals  of  the 
battery  (represented  by  P±  and  P_4  in  Fig.  10)  is 
measured  while  the  battery  is  in  action  we  no  longer 


1 1 8  ELECTROCHEM1STR  Y. 

obtain  the  true  electromotive  force  of  the  cell  P£—  P-e, 
since  part  of  the  voltage  is  used  in  sending  current 
through  the  cell  itself.  This  loss  of  voltage  in  the 
battery  is  given  by  £i=iwi,  where  w\  is  the  internal 
resistance.  If  the  measurement  is  made  when  the  circuit 
is  open,  when  i  =  o  then  £1  is  also  zero  and  we  obtain 
the  true  electromotive  force  Pe-P_£  of  the  battery. 
In  measuring  the  electromotive  force  of  a  cell,  then, 
we  obtain  the  true  value  only  when  no  current  is  flow- 
ing. A  value  slightly  smaller  is  obtained  when  the 
current  is  very  low,  and  for  this  reason  all  voltmeters 
are  made  with  a  high  resistance.  If  any  appreciable 
current  is  taken  from  the  cell  the  voltage  measured  at 
the  terminals  may  be  much  lower  than  the  true  voltage 
of  the  cell,  and  the  error  will  be  larger  the  greater  the 
internal  resistance  of  the  cell. 

Contact  Electricity. 

A  difference  of  potential  is  always  present  when  two 
different  substances  are  brought  in  contact  and  the 
surface  of  contact  is  the  seat  of  the  electromotive  force. 
Positive  electricity  is  taken  from  one  substance  and 
collected  on  the  other,  or,  what  amounts  to  the  same 
thing,  one  substance  becomes  charged  positively,  the 
other  negatively.  Chemical  reactions  are  undoubt- 
edly the  cause  of  this  contact  electricity,  but  their  nature 
has  not  been  determined  in  all  cases.  The  amounts 
of  substance  which  enter  into  chemical  reactions  under 
these  circumstances  are  so  excessively  small  that  the 
quantity  of  electricity  produced  is  also  very  small. 

It  is  a  well-known  fact  that  when  one  substance  is 
rubbed  with  another,  both  become  electrified  (frictional 


ELECTROMOTIVE  FORCE  AND   GALVANIC  CURRENT.     119 

electricity).  When  sealing-wax  is  rubbed  with  a  piece  of 
wool  the  wool  becomes  positively  electrified  ;  when  glass 
is  rubbed  with  silk,  the  silk  becomes  negatively  charged. 

No  simple  law  without  any  exceptions  has  yet  been 
discovered  with  regard  to  contact  electricity.  Sub- 
stances may,  however,  be  arranged  in  a  series  so  that 
a  body  rubbed  with  any  of  those  following  it  in  the 
series  becomes  positively  charged;  the  charges  so  pro- 
duced are  larger  the  farther  apart  the  substances  stand. 
Such  a  series  is  the  following:  glass,  wool,  silk,  wood, 
.metal,  amber,  hard  rubber,  sulphur,  shellac,  sealing- 
wax.  Coehn  has  discovered  a  law  which  seems  to  have 
pretty  general  application:  When  two  substances  are 
brought  in  contact,  the  one  whose  dielectric  constant 
is  higher  becomes  positively  electrified. 

Since  contact  and  frictional  electricity  are  of  very 
little  importance  in  chemistry  on  account  of  the  very 
small  amounts  of  electricity  concerned,  we  will  only 
mention  one  fact  in  this  connection,  which  has  lately 
become  of  technical  importance.  If  we  suspend  in 
water  some  very  finely  divided  material  such  as  powdered 
glass,  precipitates,  dyes,  peat,  etc.,  and  introduce  two 
electrodes  which  are  connected  with  a  source  of  elec- 
tricity, we  find  that  the  particles  which  become  nega- 
tively charged  are  attracted  to  the  cathode  and  deposited 
there.  This  movement  of  the  suspended  particles  is 
called  "  Endosmosis  "  or  "  Cataphosesis."  If  an  electric 
current  is  sent  through  peat  mud,  the  positively  charged 
water  moves  to  the  negative  pole,  and  this  fact  may  be 
used  for  expelling  water  from  peat.  On  the  other  hand, 
water  when  pressed  through  a  porous  diaphragm  carries 
positive  electricity  with  it,  and  so  gives  rise  to  a  current. 


I2O 


ELEC  TROCHE  MIS  TR  Y. 


Galvanic  Production  of  Current. 

If  we  wish  to  obtain  larger  quantities  of  electricity 
(without  using  a  dynamo)  we  must  use  some  arrange- 
ment in  which  the  chemical  energy  of  large  quantities 
of  material  is  converted  into  electric  energy.  This  can 
be  done  by  using  a  galvanic  cell. 

The  early  experiments  of  Galvani  on  the  twitching 
of  a  frog's  nerve  under  the  influence  of  electric-spark 
discharges  showed  that  those  same  movements  also 
occurred  when  two  metals  touched  each  other  and 
also  the  nerve.  Galvani  wrongly  attributed  this  to 
an  electric  force  in  the  nerve  itself.  Volta  found,  how- 
ever, that  the  twitching  did  not  occur  when  the  same 
metal  touched  the  nerve  at  two  points,  but  that  two 
different  metals  were  necessary.  His  classic  experi- 


+ 

Cu 


,       , 


Zn     Cu 


u 

z 

- 

; 

1 

*—* 

Zn      Cu 


FIG.  ii. 

ments  showed  further  that  two  metals  and  a  simple  salt 
solution  are  sufficient  to  produce  a  current.  He  believed 
that  the  force  producing  the  current  lay  at  the  junction 
of  the  two  metals,  but  found  further  that  a  series  of 
metals  connected  one  with  another  could  give  no  current 
in  the  absence  of  moisture,  although  they  became 
electrically  charged.  On  the  basis  of  his  discoerievs 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT,      121 

Volta  built  his  well-known  Voltaic  Pile,  which  consisted 
of  a  number  of  pairs  of  Zn  and  Cu  plates  having  between 
each  pair  a  pad  soaked  in  ordinary  salt  solution.  One 
end  of  this  arrangement  he  found  was  strongly  charged 
with  positive  electricity  and  the  other  end  with  an  equal 
amount  of  negative.  The  production  of  electricity  is 
due  to  a  reaction  between  the  solution  and  the  zinc, 
which  becomes  oxidized.  This  "  pile,"  like  the  battery 
shown  in  Fig.  n,  rapidly  loses  its  electromotive  force 
when  current  is  taken  from  it. 

Volta  placed  in  each  of  a  number  of  beakers  a  strip 
of  copper  and  one  of  zinc,  filled  the  beakers  with  dilute 
sulphuric  acid  and  connected  each 
copper  with  a  zinc  pole  as  shown 
in    Fig.    ii.     The    electromotive 
force  of  this  battery  falls  off  rapid- 
ly,  since   hydrogen  is  evolved  on 
the  copper.     The  reaction  which 
furnished  the  current  is 


In  order  to  avoid  the  evolution 
of  hydrogen  Daniell  used  a  com- 
bination of  two  metals  and  two 
solutions,  forming  the  well-known 
Daniell  element.  A  porous  porce- 
lain cell  is  filled  with  a  solu- 
tion of  copper  sulphate  and  in 
this  is  placed  a  rod  of  copper;  FlG-  I2- 

this  cell  is  then  placed  in  a  solu- 
tion of  ZnSO4  contained  in  a  glass  jar  and  a  zinc  rod  is 


122  ELECTROCHEMISTRY. 

placed  in  the  ZnSO4.*  When  the  two  metals  are  con- 
nected by  a  wire  electricity  flows  through  the  wire  from 
the  copper  to  the  zinc. 

The  reaction  which  occurs  in  the  Daniell  cell  is 


or  written  in  the  ionic  form, 

Zn+.Cu"  -»Cu+Zn". 

Copper   is  displaced  from   its  salt    by   zinc;    the   zinc 
passes  over  from  the  metallic  state  into  the  state  of  ions, 
and  copper  passes  from  ions  into  the  metallic  state. 
The  arrangement  of  the  above  cell 

Zn/ZnSO  4  -  CuSO  4/Cu 

shows  that  at  the  left  position  ions  go  into  solution  and 
at  the  right  position  ions  are  precipitated,  and  thereby 
just  as  much  positive  electricity  is  taken  away  from 
the  zinc  electrode  as  is  given  up  to  the  copper  electrode. 
This  process  goes  on,  before  the  circuit  is  closed,  until 
the  electrostatic  attraction  or  repulsion  between  the 
electrodes  and  ions  prevents  any  more  ions  from  enter- 
ing or  leaving  the  solution.  The  process*  therefore 
stops  as  soon  as  the  electromotive  force  between  the 
electrodes  corresponds  to  the  energy  of  the  reaction. 
In  the  case  of  the  Daniell  cell  the  difference  of  potential 
between  the  electrodes  is  about  i  .  i  volts. 

*  In  Fig.  12  is  shown  the  arrangement  of  a  Bunsen  cell,  which  is 
similar  to  the  Daniell  except  that  in  place  of  copper  in  copper  sulphate 
a  carbon  rod  in  HNOs  is  used.  A  number  of  other  cells,  with  the 
reactions  taking  place  in  them,  will  be  given  in  Book  II. 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT.     123 

As  soon  as  the  electrodes  are  connected  by  a  wire, 
the  two  kinds  of  electricity  flow  through  the  wire  and 
unite.  The  chemical  reaction  seeks  to  maintain  the 
two  electrodes  at  a  difference  of  potential  of  i.i  volts, 
so  that  an  uninterrupted  current  flows  through  the  wire 
from  copper  to  zinc. 

Calculation  of  Electromotive  Forces. 

The  electromotive  force  of  a  chemical  reaction  can 
only  be  calculated  in  such  cases  where  the  process  is 
a  reversible  one  (see  p.  12);  that  is,  when  the  chemical 
energy  is  converted  entirely  and  without  loss  into  elec- 
trical energy. 

The  various  formulae  no  longer  hold  when  insulation 
is  faulty,  or  when  unknown  secondary  chemical  reactions 
are  involved. 

A  chemical  reaction  is  reversible  when  it  can  be 
made  to  go  backward  and  the  system  be  restored  to 
its  original  condition  by  the  exact  quantity  of  electrical 
work  which  the  reaction  has  furnished.  The  process 
at  an  electrode  of  Cu  in  CuSCU  is  reversible.  If  we 
send  current  through  the  electrode  in  one  direction, 
copper  is  dissolved  according  to  the  scheme  Cu  — >  Cu". 
If  current  is  sent  in  the  opposite  direction  copper  is 
precipitated :  Cu  "  — >  Cu . 

The  reaction  at  an  aluminium  electrode,  Al  — » Al"',  is 
not  reversible,  because  the  reverse  reaction,  Al"'— >A1, 
does  not  take  place  in  a  water  solution.  Aluminium 
cannot  be  deposited  on  an  electrode  by  the  electrolysis 
of  a  water  solution  of  an  Al  salt.  The  H*  ions  are  dis- 
charged instead.- 


1  24  ELECTROCHEMISTRY. 

We  saw  on  p.  10  that  there  is  a  relation  between  the 
heat  of  a  reaction  and  its  electromotive  force.  If  the 
formula  which  was  derived, 


is  true  of  any  given  reaction,  then  we  may  be  sure  that 
our  experimental  arrangement  fulfils  the  condition  of 
reversibility.  In  order  to  use  this  equation  in  electrical 
calculations  it  must  be  remembered  that  the  transfor- 
mation of  i  gram  equivalent  of  any  metal  into  ions  results 
in  the  production  of  96  540  coulombs  of  electricity.  In 
the  case  of  the  Daniell  cell,  where  the  elements  Cu  and 
Zn  are  divalent,  2  Xg6  540  coulombs  are  produced  for 
every  atomic  weight  in  grams  of  zinc  which  is  dissolved. 
When  2  X  96  540  coulombs  pass  through  the  cell  65.6  grs. 
of  Zn  are  dissolved  and  63.6  grs.  of  Cu  are  deposited. 
The  work  done  by  the  cell  is  therefore  coulombs  X  vol- 
tage E  (cf.  p.  6),  and 

A  =96  540  nE, 
where  n  is  the  valence. 


Consequently  E  =  ~-  —  +  T^ 

96540^        dT 

This  is  the  well-known  Gibbs-Helmholtz  equation. 

Another  method  of  calculating  the  electromotive  force 
of  chemical  reactions  is  furnished  by  van't  Hoff's  energy 
equation  (p.  31).  Copper  is  precipitated  from  the 
solution  until  equilibrium  is  reached.  If  Ci  represents 
the  concentration  of  the  Zn  ions,  c^  that  of  the  Cu  ions 


ELECTROMOTIVE  FORCE  AND   GALVANIC   CURRENT.     125 

in  the  cell  at  the  start,  and  if  the  concentrations  of  Zn" 
and  Cu"  are  c0l  and  c0z  after  equilibrium  is  reached 
when  practically  all  the  Cu  has  been  removed  from 
solution,  then  van't  Hoff's  equation  gives 


If  n  is  the  valence  of  the  reaction  (in  this  case  2)  we 
obtain 

#96 

I 

Substituting  the  value  of  R  in  watt-seconds,  =  8.3 167 
(cf.  p.  5),  and  changing  the  natural  to  the  Briggs 
logarithm  by  multiplying  by  2-3026  we  have 

n  96  5403  =  8.3167  X2.3026T  log 
a.2£2S2§3r  iog 


For  the  ordinary  temperature  of  18°  (T  =  273  +  18)  we 
have 


The  values  of  c0l  and  c0z  are  called  the  equilibrium 
concentrations  of  the  ions.  They  may  be  determined 
if  we  allow  the  reaction  to  continue  till  it  stops  of  itself, 
and  then  measure  the  different  concentrations.  In  most 
cases,  however,  our  chemical  methods  are  not  delicate 


126  ELECTROCHEMIS  TR  Y. 

enough,  for  many  reactions  go  on  until  one  of  the  sub- 
stances seems  to  entirely  disappear. 

The  ratio  of  the  two  concentrations  J2i,  however,  may 

>a 

often  be  determined  by  electrical  methods;  for  example, 
by  measuring  the  electromotive  force  when  the  con- 
centrations c\  and  €2  are  known. 

ILLUSTRATION:  If  the  concentrations  of  Zn  and  Cu 
ions  are  made  equal  to  i,  or  if  they  are  simply  made 
equal  whatever  their  values,  then  c\  and  c2  cancel  in 
the  equation  and  we  have 


1 
bc02 

E  has  been  found  to  be  i.i  volts,  so  that  log  -^-  =38 

c  C°z 

or  -^-  =  io38;    that  is,  when  we  put  zinc  into  a  solution 


of  CuSO4  the  copper  will  be  precipitated  until  the 
concentration  of  the  zinc  ion  is  io38  times  that  of  the 
remaining  copper  ions.  For  all  analytical  purposes  this 
precipitation  is  absolutely  quantitative;  but  theoretically 
this  small  remainder  is  of  very  great  importance,  since 
otherwise  the  energy  of  this  reaction  would  be  infinite. 

As  a  second  example  we  will  calculate  the  electro- 
motive force  of  a  Daniell  cell  in  which  c\  =  i  and  c%  =  o.ooi  ; 
then  we  have 

£  =  0.02-9  l°g  Io38  —  > 

or 

12=  i.i  +0.029  log  o.ooi  =  1.013  volts. 

In  a  similar  way,  if  we  know  the  electromotive  force 


ELECTROMOTIVE  FORCE  AND   GALYANIC  CURRENT.     127 

for  some  particular  concentration  we   can   calculate  it 
for  any  concentration. 

Nernst  has  given  the  name  "  electrolytic  solution 
pressure  "  to  the  values  c0l  and  c02.  The  meaning  of 
this  term  will  be  considered  in  the  next  section. 

Nernst's  Formula. 

Every  substance  has  a  certain  tendency  to  change  over 
fro"  i  the  condition  in  which  it  happens  to  be  to  some 
of  er.  This  tendency  has  been  given  the  name  of 
"  fugacity."  For  instance,  liquid  water  has  a  tendency 
to  pass  over  into  water  vapor,  and  water  vapor,  on  the 
other  hand,  strives  to  condense  and  reform  liquid  water. 
If  the  first  tendency  prevails  evaporation  actually  takes 
place.  The  fugacity  is  dependent  on  the  temperature, 
but  at  constant  temperature  is  higher  the  higher  the 
concentration,  or  in  the  case  of  condensation,  the  higher 
the  vapor  density. 

When  a  'solid  soluble  salt  is  brought  in  contact  with 
water  it  strives  to  pass  over  into  the  dissolved  condition. 
The  concentration  of  the  solid  salt  is  constant  and  con- 
sequently the  fugacity  of  a  solid  salt  is  constant.  On 
the  other  hand  the  salt  which  has  already  dissolved 
has  a  tendency  to  leave  the  solution  and  go  back  to  the 
solid  state,  and  this  tendency  is  greater  the  higher  the 
concentration  of  the  solution  is.  The  actual  force  which 
causes  the  salt  to  dissolve  is  equal  to  the  difference  be- 
tween the  two  fugacities  and  is  therefore  smaller  the  more 
concentrated  the  solution  is.  Finally  the  concentration 
of  the  solution  reaches  a  value  where  the  two  fugacities 
balance,  then  no  more  salt  dissolves  and  the  solution  is 


128  ELECTROCHEMIS  TR  Y. 

saturated.  If  the  concentration  is  too  high,  i.e.,  if  the 
solution  is  supersaturated,  the  tendency  to  take  the  solid 
form  overcomes  the  tendency  to  dissolve  and  the  re- 
action goes  in  the  reverse  direction. 

Very  similar  relations  hold  for  the  metals.  They  all 
have  a  tendency  to  pass  over  into  the  form  of  ions,  and 
this  tendency  is  constant  as  long  as  solid  metal  is  present, 
for  the  active  mass  of  a  metal  is  constant.  On  the  other 
hand,  the  ions  strive  to  pass  back  into  the  metallic  con- 
dition, and  their  tendency  to  do  so  varies  according  to 
their  concentration.  We  represent  the  first  value  by  P,  the 
solution  pressure,  as  PZn,  PCW  PAS,  etc.;  the  deionizing 
tendency  will  be  represented  by  p,  and  is  nothing  less 
than  the  osmotic  pressure  of  the  ions.  The  osmotic 
pressure  and  deionizing  tendency  both  strive  to  make 
the  solution  more  dilute. 

As  in  the  reaction  of  a  salt  going  into  solution,  a 
precipitation  of  the  metals  actually  takes  place,  according 
as  P  or  p  has  the  higher  value,  but  the  one  essential 
point  of  difference  lies  in  the  fact  that  the*  metals  can 
only  go  into  solution  in  the  form  of  positively  charged 
ions  and  thus  carry  positive  electricity  with  them.  Con- 
sequently the  passage  of  the  metal  from  the  solid  to  the 
dissolved  state  leaves  the  remaining  metal  negatively 
charged  (or  if  p  >  P,  the  resulting  solid  metal  is  positively 
charged)  and  the  electrostatic  attraction  (or  repulsion) 
thus  produced  soon  puts  a  stop  to  any  further  solution 
(or  deposition). 

The  following  three  cases  are  possible,  illustrated  by 
Figs.  13,  14,  and  15.  IiP>p  traces  of  metal  will  go  into 
solution  and  the  metal  takes  on  a  negative  charge.  If 
P<P  a  few  ions  separate  out  on  the  metal  and  give  it 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT.      129 

a  positive  charge,  leaving  the  solution  negative.  If 
P  =  p  no  changes  occur. 

If  we  can  arrange  so  as  to  conduct  the  electricity 
away  from  the  solution  and  the  electrode,  the  influence 
of  the  electrostatic  charge  disappears  and  considerable 
quantities  of  metal  may  go  into  solution  or  be  deposited, 
according  as  the  conditions  are  those  represented  by 
Fig.  13  or  Fig.  15. 

These  two  processes  can  furnish  a  certain  amount  of 


work.     When   a   substance    changes    its    pressure   from 
P  to  p  the  work  to  be  obtained  is 

A=RTlnj  (cf.  p.  21). 

Since  the  solution  or  deposition  of  i  equivalent  of 
any  metal  is  accompanied  by  the  passage  of  96  540 
coulombs,  and  that  of  a  mol  of  any  metal  by  96  540^, 
where  n  is  the  valence,  and  since,  further,  the  work 
obtainable  is  measured  by  the  electromotive  force  X 
the  number  of  coulombs,  we  have 

p 

—. 

If  we  simplify  this  expression  in  the  same  way  as  the 
corresponding  one  on  p.  121  we  obtain 


13° 


ELEC  TROCHE  MIS  TR  Y. 


Now  it  is  possible  to  find  a  concentration,  c0,  at  which 
the  osmotic  pressure  of  the  ions  just  balances  the  solution 
pressure  of  the  metal,  and  the  condition  of  things  is  as 
represented  in  Fig.  14.  c0  corresponds  to  the  solution 
pressure  P,  and  if  c  represents  the  concentration  at  which 
the  osmotic  pressure  of  the  ions  is  p,  then 


and     E= 


E  is  the  electromotive  force  with  which  the  metal  seeks 
to  go  into  solution  when  the  concentration  of  the  ions 
is  c,  and 


is  the  electromotive  force  in  a  solution  when  the  ions 
have  a  concentration  of  one,  i.e.,  i  mol  per  Utre.  E\ 
is  called  the  electrolytic  potential  of  the  metal. 

If  the  concentration  of  the  ions  of  a  metal  is  changed 

by  a  power  of  10,  tlie  potential  changes  by volts 

n 

at  ordinary  temperature. 

We  will  now  combine  two  systems,  each  consisting 
of  a  metal  dipping  in  a  solution  of  one  of  its  salts,  the 
two  solutions  being  separated  by  a  porous  diaphragm 
which  hinders  the  two  solutions  from  mixing,  but  does 
not  prevent  the  passage  of  the  current.  The  condition 
of  the  system  is  as  follows  (Fig.  16):  metal  I  becomes 
charged  negatively,  since  its  solution  pressure  P\  is 


ELECTROMOTIVE  FORCE  AMD   GALVANIC  CURRENT.     13* 

greater  than  the  osmotic  pressure  p,  of  the  metallic  ions 
in  the  solution;  metal  II  becomes  positively  charged, 
since  p2  is  greater  than  P2.  There  will  therefore  be 
a  certain  difference  of  potential  between  the  two  metals. 
If  the  metals  are  connected  for  an  instant  by  a  wire, 
the  charges  on  the  two  electrodes  unite.  The  electro- 
static repulsion  and  attraction  at  the  electrodes  dis- 


FIG.  16. 

appears,  and  traces  of  metal  I  again  go  into  solution 
and  traces  of  metal  II  are  precipitated  until  the  electro- 
static forces  again  stop  the  process.  If  we  allow  the 
electrodes  to  remain  connected  a  continuous  current 
will  flow  through  the  wire,  metal  I  will  continue  to  be 
dissolved  and  metal  II  to  be  precipitated.  The  Daniell 
cell  is  an  arrangement  of  this  sort. 

How  much  work  can  such  an  element  do,  and  what 
is  its  electromotive  force?     Evidently 


°-°577  !          Pi 

~  log     - 


0.0577 


,    a 

log      - 


If  the  two  metals  have  the  same  valence  (ni=n2=n) 
as  in  the  Daniell  cell,  then,  if  we  put  c0:c  =  P:p, 


log 

B 


n 


132  ELECTROCHEMISTRY. 

which  is  identical  with  van't  Hoff's  equation  on  p.  125. 
If  P2  is  also  greater  than  p2  for  the  second  metal,  then 


2  2 

or,   since  log  —  =  —  log  ~~»   this   equation   is    identical 

p2  *2 

with  the  one  first  given.  In  this  case  the  two  metals 
are  both  negatively  charged  before  the  circuit  is  closed, 
but  to  a  different  degree,  and  this  difference  causes 
the  current  to  flow  on  completing  the  circuit.  The 
positive  current  flows  through  the  wire  from  the  metal 

P 

having  the  lower  value  of  —  to  the  other;    this  latter 

therefore  dissolves  and  the  first  is  deposited. 
When  the  concentration  of  the  ions  is  the  same  in 

both  compartments  of  the  cell,  —  =i  and  we  have 


0.0577        Pl 
E=____log_ 

The  electromotive  force  E  of  such  a  cell  furnishes  a 

p 
means  of  calculating  the  fratio  of  -5-. 

f  2 

In  order  to  determine  the  actual  separate  values  of 
PI  and  P£  we  must  use  some  combination  of  metal  and 
solution  where  P  =  p.  Unfortunately  no  such  combina- 
tion is  known  with  certainty,  and  we  are  obliged  to  resort 
to  the  same  principle  which  is  used  in  deciding  on  the 
atomic  weights,  i.e.,  we  must  fix  an  arbitrary  unit.  We 


UNlvtKbllY 

OF 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT.     133 


do  not  know  the  actual  weight  of  the  atoms;  what  we 
measure  is  the  relative  weight.  We  arbitrarily  take  16 
as  the  atomic  weight  of  oxygen  and  use  this  as  the 
standard. 

Following  a  suggestion  of  Nernst's,  we  arbitrarily  take 
the  solution  pressure  of  hydrogen  as  onet  so  that 

0.0577  log  1=0. 

To  determine  the  electrolytic  solution  pressure  of  the 
other  metals  we  measure  the  electromotive  force  of 
cells  built  up  in  this  way: 

'  solution  —  wMetal*  solution|Metal. 


A  platinum  electrode  over  which  bubbles  of  hydrogen 
gas  are  passed,  dipping  in  an  acid  solution  whose  H' 
ion  concentration  is  i  (normal),  is  combined  with  a  metal 
dipping  into  a  solution  of  one  of  its  salts  of  such  strength 
that  the  ionic  concentration  is  one  and  the  electromotive 
force  of  the  whole  combination  is  measured.  A  platinum 
electrode  saturated  with  hydrogen  gas  behaves  as  regards 
its  electromotive  force  as  if  made  of  the  metal  hydrogen 
(cf.  p.  136).  If  we  find  that  the  combination 

PtHJ»H--nAg-  Ag 

has  an  electromotive  force  of  —0.771  -volt,  then  the 
electrolytic  potential  of  silver  is  —0.771.  The  minus 
sign  is  used  because  hydrogen  has  a  higher  solution 
pressure  than  silver,  and  the  current  flows  in  the  con- 
necting wire  from  the  silver  to  platinum.  In  the  com- 
bination 

PtH2  nR'-nZn'  |Zn 


134  ELECTROCHEMISTRY. 

the  voltage  is  +0.770;  here  the  current  flows  in  the 
opposite  direction.  From  these  two  values  we  find 
the  electromotive  force  of  the  combination 

Zn\nZn"  —  wAg'|Ag 

to  be  0.770—  (  —  0.7  71)  =  1.541  volts.  The  positive  sign 
is  given  to  the  potential  of  those  metals  whose  solution 
pressure  is  higher  than  that  of  hydrogen,  since  they  have 
a  greater  power  for  taking  on  a  positive  charge;  metals 
whose  solution  pressure  is  less  than  that  of  hydrogen, 
and  also  elements  or  radicals  .which  take  on  a  negative 
charge,  have  a  negative  potential.  The  same  thing  is 
meant  when  we  speak  of  the  "  nobility  "  of  the  metals; 
silver  is  more  noble  than  zinc,  and  zinc  is  less  noble  than 
hydrogen,  etc. 

Now  the  hydrogen  electrode  is  not  so  easily  reproducible 
as  certain  other  electrodes  which  are  known,  and  which 
would  naturally  be  chosen  as  standards  in  determining 
the  exact  values  of  the  different  potentials.  The  easiest 
electrode  to  make,  and  one  which  always  has  the  same 
potential  is  the  "  normal  calomel  electrode," 


The    calomel    electrode   has    a    potential   of    —0.283 
against  the  hydrogen  electrode,  i.e.,  an  element  of  the 

form 

H  solution  -wKCl  +  HgCl|Hg 


has  an  electromotive  force  of  —0.283  volt,  and  in  it  the 

*  (Cf.  p.  18  and  the  chapter  on  Methods  of  Measurement  in  Book  II 
for  details  concerning  the  calomel  electrode  and  certain  other  normal 
electrodes.) 


ELECTROMOTIVE  FORCE  AND   GALVANIC  CURRENT.     135 


positive    current    goes    through    the    solution    from    the 
hydrogen  to  the  mercury  electrode. 

The  numbers  in  the  following  table  have  been  obtained 
with   the   help   of   such   normal   electrodes.     Column   i 


Calomel 
Electrode 
=  —0.283 
Hydrogen 
Electrode 

=  0.0 

Calomel 
Electrode 
=  —0.56 
'  Absolute" 
Potentials 

Mn.  . 

+  1.075 

+  0.798 

Zn  

+  0.770 

+  o  .  493 

Cd  

+  0.420 

+  0.143 

Fe  

+  0.344 

+  o  .  067 

Tl 

+  O    322 

+  o  .  045 

Co 

'   w  .  £4.  & 

+  o.  232 

Ni.  .  .  .  :  

+  0.228 

—  o  .  049 

Pb  

+  o.  151 

—  0.132 

H  

±0.0 

-0.277 

Cu  

-0.329 

-0.606 

Hg  

-o-753 

-1-030 

Ag  

-0.771 

-  1  .  048 

Cl  

—  I  .  7C7 

—  i  6^6 

Br 

ooo 
—  o  003 

—  I     27O 

T 

**  •  Wo 
—  o  ^20 

.  A  j\j 
—  O   707 

\J  .  ^  ^  w 

<_>  .  ^y  i 

contains  the  electrolytic  potentials  of  the  different  ele- 
ments; the  second  column  contains  the  same  values  all 
shifted  0.277  v°lt  m  order  to  refer  them  to  another 
standard  proposed  by  Ostwald.* 

We  can  obtain  from  this  table  the  electromotive  force 
of  any  cell  of  the  Daniell  type.  For  instance,  a  copper- 
nickel  element,  in  which  the  concentration  of  the  metallic 

*  According  to  a  theory  of  Helmholtz,  the  surface  tension  of  polarized 
mercury  has  a  maximum  value  when  there  is  no  difference  between  its 
potential  and  that  of  the  solution.  This  theory,  however,  has  not  been 
satisfactorily  proven;  it  appears  that  the  surface-tension  phenomena  of 
polarized  mercury  are  more  complicated  than  Helmholtz  supposed. 


136 


ELECTROCHEMISTRY. 


ions  of  each  salt  is  equal,  has  an  electromotive  force  of 
+  0.288— (  —  0.329)  =  0.557  volt.  A  Zn-Pb  cell  has  a 
voltage  of  0.619,  Zn  — Cu,  i.e.,  the  Daniell  cell,  has 
1.099  volts,  Cu— Ag  0.442  volt,  etc. 

Gas  Electrodes. — If  we  take  an  electrode  of  platinum 
which  has  had  deposited  on  it  a  coating  of  finely  divided 
platinum  and  allow  bubbles  of  hydrogen  to  pass  up 
over  it,  some  of  the  gas  dissolves  in  the  platinum  and  the 
electrode  behaves  electrochemically  as  if  it  were  composed 
of  the  metal  hydrogen.  Every  chemist  knows  that  most 
gases,  hydrogen  particularly,  are  chemically  much  more 
active  in  the  presence  of  finely  divided  platinum 
(Pt  "  sponge  ").  This  is  probably  due  to  the  fact  that 
hydrogen  dissolved  in  Pt  is  partially  dissociated  into 
atoms,  H2  =  H  +  H,  and  the  atoms  enter  into  reaction 
much  more  readily  than  the  H2  molecules.  The  quantity 
of  hydrogen  which  dissolves  in  the  Pt,  i.e.,  its  concen- 
tration or  active  mass,  is  dependent  on  the  pressure 
which  is  exerted  on  the  hydrogen  above  the  solution. 
This  follows  from  Henry's  absorption  law,  which  states 
that  the  solubility  of  a  gas  in  a  liquid  or  solid  is  pro- 
portional to  the  concentration  of  the  gas,  and  this  in 
turn,  according  to  Boyle's  law,  is  directly  proportional 
to  the  pressure  on  the  gas. 

To  calculate  the  electromotive  force  of  gas  electrodes 
we  again  make  use  of  van't  Hoff's  equation,  but  we  must 
remember  that  in  previous  cases  the  active  mass  of  the 
metals  were  constants  and  therefore  cancelled  out  in 
the  fraction  after  the  log.  In  the  case  of  gases,  however, 
the  active  masses  do  not  thus  disappear;  they  are  not 
constants,  but  are  dependent  on  the  pressure. 

Let  us  consider  two  hydrogen  electrodes  at  atmospheric 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT.     137 

pressure  in  a  solution  whose  H*  ion  concentration  is 
ci,  then 

RT    CA     RT    CA 

E  =  -  In  —  —  -  In  —  =  o. 

2          C\  2          Ci 

CA  is  the  active  mass  of  the  hydrogen  dissolved  in  the  Pt 
at  atmospheric  pressure  P.  The  2  in  the  denominator 
is  due  to  the  fact  that  H2  has  a  valence  of  2.  If  we 
combine  an  electrode  under  atmospheric  pressure  with 
another  under  the  pressure  p,  in  which  the  active  mass 
of  the  hydrogen  is  CPJ  we  have 


RT    Cp     RT    CA 

E  =  -  In—2  —  -  In  —  , 

2          Ci  2          Ci 


or  since  CP:CA  = 


If  p>P  the  current  in  the  solution  goes  from  the  p 
electrode  to  the  P  electrode  ;  if  p  <  P  it  goes  in  the  opposite 
direction,  that  is,  the  electrode  which  has  less  hydrogen 
gets  more  from  the  passage  of  the  current,  and  this  will 
continue  till  the  pressure  at  both  electrodes  becomes 
the  same.  If  the  pressures  p  and  P  are  kept  constant 
the  cell 

Pt  with  H2  under  pressure  P\  solution  |Pt  with  H2  under  pressure  p 

will  furnish  a  steady  current.  The  reactions  at  the  elec- 
trodes are 

H2->2H-    or     2H-^H2 

according   to   the  direction  of  the   current.     This   is   a 


13&  ELECTROCHEMISTRY. 

"  concentration  cell "  in  which  the  current  is  due  to  a  dif- 
ference in  concentration  of  the  substances  forming  the 
electrodes.  If  the  pressure  is  changed  by  a  power  of 

.  0.058 
10  the  potential  is  changed  =  0.029  vo^- 

Other  gases  when  dissolved  in  Pt  act  similarly  to 
hydrogen  in  their  electrochemical  relations.  A  platinum 
electrode  saturated  with  chlorine  behaves  like  an  electrode 
of  the  element  chlorine,  and  its  potential,  which  is  —1.35 
at  atmospheric  pressure,  changes  with  the  pressure  in  the 
same  way  as  that  of  the  hydrogen  electrode.  The  oxygen 
electrode  also  changes  its  potential  with  the  pressure, 
but  we  must  remember  that  in  this  case  the  molecule 
O2  has  a  valence  of  four. 

From  the  values  for  the  potentials  of  the  metalloids 
as  given  in  the  table  on  p.  135  we  can  derive  the  electro- 
motive force  of  any  cell ;  for  instance,  the  cell 

Zn|ZnCl2|PtCi2 

has  an  electromotive  force  of  2.12  volts;    the  voltage 
with  which  chlorine  displaces  iodine  from  a  solution  of 
an  iodide  is  1.35  —  0.52=0.83  volt  when  the  concentration 
of  chlorine  and  iodine  ions  is  normal. 
The  Grove  gas-cell, 

O2 1  solution  |H2, 

has  a  voltage  of  1.12.  This  value  for  the  potential  of 
O2  refers  to  a  solution  when  the  concentration  of  H* 
ions  is  normal.  We  cannot  calculate  the  true  potential 
of  oxygen  in  a  solution  which  is  normal  with  respect 


ELECTROMOTIVE  FORCE  AMD   GALVANIC   CURRENT.     139 

the  O"  ions,  for  at  present  we  do  not  know  the  con- 
centration of  the  O"  ions  in  any  solution  with  any  degree 
of  certainty. 

Potential  of  Alloys.  —  The  dependence  of  the  electro- 
motive force  on  the  concentration  of  the  substances 
forming  the  electrodes  is  also  seen  in  the  case  of  metals 
which  form  alloys.  Suppose  we  have  a  cell  whose 
electrodes  are  composed  of  dilute  zinc  amalgams  whose 
zinc  concentrations  are  different,  and  in  which  the 
electrolyte  is  a  solution  of  ZnSO4;  the  electromotive 
force  of  such  a  cell  is,  as  above, 


Here  P2  and  PI  are  the  solution  pressures  of  the  zinc 
in  the  amalgams,  and  since,  as  in  the  case  of  Pt  and  H2, 
we  may  consider  zinc  as  the  dissolved  substance  and 
mercury  as  the  solvent,  we  have  P^'-Pi^c^Ci,  where 
€2  and  Ci  are  the  zinc  concentrations  in  the  amalgams. 
We  have  therefore 


This  formula  has  been  verified  experimentally.  We 
have  assumed  in  the  above  formula  that  the  molecules 
of  the  dissolved  zinc  are  composed  of  single  atoms.  If 
this  were  not  the  case,  and  the  molecules  were  composed, 
say,  of  two  zinc  atoms,  Zn2,  then  we  would  have  to  divide 
R  T  by  4  to  get  the  electromotive  force.  But  since  the 
formula  as  written  represents  the  experimental  facts, 
this  in  itself  furnishes  a  proof  that  the  zinc  molecules 
when  dissolved  in  mercury  are  composed  of  single  atoms. 


HO  ELECTROCHEMISTRY. 

The  amalgams,  or  in  general  the  alloys,  may  be 
divided  into  three  classes: 

1.  The    metals    form    a    mechanical    mixture.     Such 
mixtures  have  the  potential  of  the  "  less  noble  "  metal. 
For  instance  a  mixture  of  Zn  and  Fe  has  the  potential 
of  pure  zinc. 

2.  The  metals  form  a  solution   (amalgam  or  alloy). 
A  metal  solution  is  always  "  nobler,"  i.e.,  has  a  potential 
nearer  that  of-  oxygen,  than  its  least  noble  component, 
and  the  greater  the  amount  of  work  which  results  from 
the  formation  of  the  alloy  the  nearer  will  its  potential 
approach  that  of  oxygen. 

3.  The   metals   form   a  chemical  compound.     In  this 
case  the  electrode  has  its  own  particular  solution  pres- 
sure, and  the   ions  it  sends  into  solution  are  formed  in 
the  same  proportion  as  the  elements  exist  in  the  elec- 
trodes. 

These  various  conditions  have  to  be  considered  in 
the  electrolytic  solution  of  impure  metals;  for  instance, 
in  the  refining  of  crude  copper,  silver,  and  gold.  Details 
concerning  the  solution  of  alloys  and  the  refining  of 
the  metals  will  be  given  in  Books  II  and  III. 

Potential  of  Compounds. — Case  3,  mentioned  above, 
has  a  very  general  application.  Every  element  when 
entering  a  compound  attains  an  entirely  different  potential. 
For  instance,  chlorine  has  a  very  different  potential, 
according  as  it  is  present  as  the  free  element,  or  a  as 
solution  in  platinum,  or  as  a  chloride,  and  its  potential 
is  changed  to  a  larger  degree  according  to  the  amount 
of  free  energy  developed  in  the  formation  of  the  compound. 

As  may  be  seen  from  the  table  on  p.  135,  AgCl  has  a 
lower  potential  of  formation  than  CuCl,  i.e.,  its  chlorine 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT.     141 

potential  is  higher  than  that  of  CuCl.     This  will  be 
clearer  when  we  remember  that  the  reaction 


like  all  reactions,  goes  on  only  till  a  certain  state  of  equi- 
librium is  reached.  All  the  chlorine  does  not  enter  into 
combination,  but  an  excessively  small  quantity  of  Ag 
and  Cl2  remains  free.  This  small  remainder  may  react 
like  chlorine  at  an  exceedingly  low  concentration,  and 
silver  chloride  will  have  a  chlorine  potential  correspond- 
ing to  this  concentration  of  C\2,  i.e.,  its  electromotive 
force  will  be  that  of  a  chlorine  electrode  at  very  low 
pressures.  The  more  stable  a  compound  is,  i.e.,  the 
higher  the  voltage  of  the  cell 

Metal  j  solution  of  the  chloride  of  the  metal  |  chlorine 

is,  the  more  complete  is  the  reaction  and  the  lower  the 
chlorine  pressure  and  chlorine  potential. 

An  electrode  made  of  a  metal  covered  with  its  solid 
chloride  has  a  perfectly  definite  potential  and  is  re- 
versible with  respect  to  chlorine.  For  instance,  the 
electrode 

Hg/HgCl  +  wKCl 

has  a  potential  of  —0.283  volt.  If  current  passes  from 
left  to  right  HgCl  is  formed;  if  in  the  reverse  direction, 
chlorine  goes  into  solution  and  HgCl  disappears.  Elec- 
trodes like  this  which  are  reversible  with  respect  to 
the  anion  are  called  electrodes  of  the  second  kind,  while 
those  reversible  with  respect  to  the  metal  are  called 
electrodes  of  the  first  kind.  Electrodes  of  the  second 


142 


ELECTROCHEMIS  TR  Y. 


kind  are  very  often  employed  in  potential  measurements 
on  account  of  their  constancy.  The  calomel  electrode 
is  the  one  most  used.  The  potential  varies  with  the 
concentration  of  the  CY  ions  in  the  solution  according 
to  the  same  formula  as  for  the  metals, 


n        D  c 

where  —  -  log  P  is  the  potential  of  the  electrode  when 
ti 

the  concentration  of  the  CF  ions  in  the  solution  is  i. 
Reversible  electrodes  for  other  metalloids  or  radicals 
can  be  made  in  the  same  way  ;  for  instance, 

Ag/Agl  +  KI     or    Hg/Hg2SO4+H2SO4,  etc. 

Salts  which  are  the  least  soluble  in  water  are  naturally 
chosen  for  use  in  normal  electrodes.  The  following 
table  gives  the  potentials  of  some  electrodes  of  this  sort: 


Hydrogen 
Electrode 

=  0 

Calomel 
Electrode 
=  —0.56 

Pb/PbSO    +  1  O4wH2SO 

0.284 

o  007 

Hg/Hg2SO4+  1  .owK2SO4  
Hg/Hg2Cl2  +  1  owKCl 

-0.644 
—  o  283 

—  0.921 
—  o  560 

Hg/Hg2Cl2  +o.  iwKCl  
Ag/AgCl      +i  owKCl 

-0.338 
—  O    2OO 

—  0.614 
—  o  483 

Ag/AgCl      +o  iwKCl  

—  o.  263 

—  o.  540 

The  values  given  in  this  table  are  to  be  used  in  the 
same  way  as  those  given  on  p.  135,  so  that  a  cell  con- 
sisting of  Zn  in  ZnSC>4  combined  with  a  mercurous 
sulphate  electrode  will  have  a  voltage  of  0.77+0.644  = 
1.414  volts. 


ELECTROMOTIVE  FORCE  AND   GALVANIC  CURRENT.     143 

The  so-called  oxidation  and  reduction  potentials  are 
to  be  considered  in  a  similar  way.  A  Pt  electrode  cov- 
ered with  potassium  chlorate  (KC1O3)  has  a  perfectly 
definite  potential,  for  the  chlorate  has  a  definite  oxygen 
pressure,  due  to  the  incompleteness  of  the  reaction  which 
has  produced  the  chlorate.  The  Pt  electrode  becomes 
charged  with  oxygen  at  this  pressure  and  thus  becomes 
an  oxygen  electrode,  which  can  bring  about  reactions  of 
oxidation.  The  potential  of  such  a  secondary  oxygen 
electrode  corresponds  to  the  pressure  with  which  the 
oxidizing  agent  tends  to  give  up  oxygen.  The  potential 
of  a  Pt  electrode  in  a  solution  of  an  oxidizing  agent, 
therefore,  is  due  simply  to  a  charge  of  gaseous  oxygen 
furnished  by  the  oxidizing  agent,  as  Nernst  has  proven 
experimentally. 

The  reduction  potential  of  reducing  agents  is  due  to 
exactly  similar  causes.  Reducing  agents  give  up  H2 
to  a  Pt  electrode,  or,  what  amounts  to  the  same  thing, 
they  abstract  oxygen,  until  the  gas  concentration,  and 
consequently  the  potential,  reaches  a  value  corresponding 
to  the  reducing  power  of  the  substance.  If  we  bring 
together  on  a  Pt  electrode  an  oxidizing  agent,  such  as 
KMnC>4  and  a  reducing  agent,  such  as  FeC^,  the  per- 
manganate gives  up  oxygen  to  the  electrode  and  the 
FeCl2  takes  it  away;  that  is,  the  second  substance  becomes 
oxidized  by  the  first.  The  potential  with  which  this 
reaction  takes  place  is  simply  the  difference  between 
the  oxidation  potentials  of  the  two  substances.  These 
potentials  are  dependent  on  the  concentrations  of  the 
oxidizing  and  reducing  agents  and  may  be  calculated 
by  Nernst's  equation.  Data  and  information  concerning 
the  use  of  a  number  of  oxidation  and  reduction  electrodes 


1 44  ELE  C  TROCH^  MIS  TR  Y. 

will  be  given  in  Book  II.  The  Grove  gas-cell,  for  instance, 
is  an  oxidation-reduction  cell,  consisting  of  the  oxidizing 
agent  oxygen  and  the  reducing  agent  hydrogen. 

Concentration  Cells.  —  A  kind  of  concentration  cell 
differing  from  that  on  p.  139  is  the  following: 

Ag|AgN03-AgN03|Ag, 
ci  £2 

i.e.,  electrodes  of  the  same  metal  dipping  into  solutions 
of  a  salt  of  the  metal  having  different  concentrations. 
The  current  through  the  solution  flows  from  the  less 
concentrated  to  the  more  concentrated  solution.  On 
one  side  silver  is  dissolved,  on  the  other  precipitated, 
until  the  concentration  on  both  sides  is  the  same.  If 
we  neglect  on  account  of  its  smallness  the  difference  of 
potential  at  the  point  of  contact  of  the  two  solutions — 
as  we  have  always  done  hitherto — the  electromotive 
force  at  18°  is  given  by 

E  =  RTln— =  0.0577  log  — . 

C-2  €2 

The  solution  pressure  of  the  metal,  being  the  same  at 
each  electrode,  does  not  appear  in  the  formula. 

In  many  cases  the  electromotive  force  at  the  junction 
of  the  two  solutions  may  be  neglected,  but  not  always. 
The  following  consideration  will  show  the  cause  of  this 
electromotive  force  and  how  to  calculate  it.  Two  so- 
lutions of  different  concentration  always  strive  to  dif- 
fuse into  each  other  till  the  concentration  is  the  same 
at  all  points.  When  a  dissolved  salt  diffuses  the  ion 
having  the  highest  velocity  tends  to  move  on  ahead  of 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT.     MS 

the  other.  In  the  case  of  acids  this  is  the  hydrogen  ion 
which  has  the  highest  velocity  of  any  of  the  ions.  This 
partial  separation  of  the  ions  can  only  take  place  to  an 
immeasurable  extent,  for  since  the  more  dilute  solution 
has  an  excess  of  H'  ions,  the  electrostatic  attraction  of  the 
ions  gives  rise  to  a  force  which  compels  the  two  kinds  of 
ions  to  remain  together.  As  a  result,  in  the  diffusion  of 
a  salt  the  more  rapid  ion  is  held  back  and  the  slower  is 
accelerated.  This  tendency  of  one  ion  to  hurry  on  ahead 
of  the  other  gives  rise  to  an  electromotive  force  which, 
as  Nernst  has  shown,  can  be  calculated  from  the  velocity 
of  the  ions.  If  u  represents  the  velocity  of  the  cation 
and  v  that  of  the  anion,  then 


C2 


e  being  the  difference  of  potential  at  the  junction  of  two 
solutions  whose  concentrations  are  c\  and  c<2;  the  salt  in 
each  solution  is  supposed  to  be  completely  dissociated  and 
the  ions  all  univalent.  This  formula  holds  only  for  1:1 
salts  (cf.  p.  96);  the  formulae  for  others  are  more  com- 
plicated, and  most  of  them  have  not  been  derived.* 

From  the  theory  of  the  diffusion  of  electrolytes  it 
follows  that  this  electromotive  force  at  the  junction 
of  two  solutions  of  different  concentration  practically 
disappears  when  each  solution  contains  equal  amounts 
of  another  salt  whose  concentration  is  much  higher. 
To  avoid  this  somewhat  uncertain  contact-electromotive 

*  For  further  particulars  see  the  list  of  text-books  named  at  the  close 
of  this  volume:  in  particular  Nernst,  Theoretische  Chemie,  4th  edition, 
p.  699. 


146  ELECTROCHEMIS  TR  Y. 

force  a  large  excess  of  some  indifferent  salt  is  often 
added. 

Applications  of  Nernst's  Formula. — The  formula  on  p. 
144  has  been  experimentally  verified  in  a  great  number 
of  cases,  and  may  be  used  to  determine  the  solubility  of 
certain  difficultly  soluble  salts  in  cases  where  the  solubility 
is  too  small  to  be  measured  by  chemical  means.  We 
find,  for  instance,  that  the  electromotive  force  of  the  cell 
Ag|o.ooi  n  AgNO3  +  i.owKNO3-i.o  n  KNO3+AgI|Ag 
is  0.22  volt.  The  concentration  of  the  silver  ions  on 
the  left  is  o.ooi ;  let  that  on  the  right  be  c  where  c  is  the 
value  sought.  From  the  formula 

o.ooi 
0.22  =0.0577  log 

we  find  that  c  =  i.6Xio~8,  i.e.,  a  litre  of  a  saturated 
Agl  solution  contains  1.6  X  i o~8  mols  of  Agl  =  0.000003 5 
gr.  Agl.  This  agrees  very  well  with  the  value  i.5Xio~8 
obtained  from  conductivity  measurements. 

Another  very  important  application  of  the  measure- 
ment of  concentration  cells  is  in  determining  the  disso- 
ciation constant  of  water,  a  method  already  mentioned 
on  p.  72. 

The  cell 

PtH2|NaOH-HCl|PtH2 

is  called  the  "  neutralization  cell  "  because  the  reaction 
of  neutralization  is  the  one  which  furnishes  the  current 

NaOH  +  HC1  =  NaCl + H2O, 
or  more  correctly,  as  we  saw  on  p.  66, 


ELECTROMOTIVE  FORCE  AND  GALVANIC  CURRENT,     14? 

The  voltage  of  this  cell  with  o.i  n  solutions  is  0.6460  at 
25°  To  this  0.0468  volt  must  be  added,  because  at  the 
contact  of  the  two  solutions  there  is  an  opposing  electro- 
motive force  of  this  value.  The  voltage  of  the  cell 
without  this  "  diffusion "  voltage  would  therefore  be 
0.6928.  The  concentration  of  the  H'  ions  in  a  o.i  n 
solution  of  HC1  is  0.0924,  that  of  the  OH'  ions  in  a  o.i 
n  solution  of  NaOH  is  0.0847,  as  found  from  conductivity 
measurements. 

The  cell  is  to  be  considered  as  a  concentration  cell 
with  respect  to  the  H*  ions,  and  therefore  follows  the 
formula  on  p.  144.  Introducing  the  different  values 
we  have 

o  0024. 

0.6928  =  0.05898  log  -     — , 
c 

where  c  is  the  concentration  of  the  H'  ions  in  the  NaOH 
solution,  c  is  found  to  be  i.66Xio~13.  Therefore 

[H'][OH']=i.4o6Xio-14    and    c0  =  i.i87Xio-7, 

which  is  in  excellent  agreement  with  the  values  obtained 
by  other  methods  (cf.  p.  65  and  also  p.  91). 

Secondary  Elements  and  the  Accumulator. 

The  secondary  elements  do  not  differ  in  principle  nor 
in  the  calculation  of  their  electromotive  forces  from  the 
primary  elements  which  we  have  just  studied.  They 
are  nominally  distinguished  from  the  first,  however, 
because  after  they  are  once  used  up  they  may  be  revived 
or  recharged  by  sending  a  reverse  current  of  electricity 
through  them,  and  it  is  not  necessary  to  rebuild  them  of 


1 48  ELEC  TROCHE  MIS  TR  Y. 

fresh  material  as  in  the  case  of  primary  cells.  The 
oxygen-hydrogen  cell 

Pto2  |solution|PtHa 

may  be  considered  as  a  secondary  cell  if  the  gases  re- 
sulting from  the  electrolysis  are  collected  at  the  electrodes 
and  then  used  to  produce  a  current. 

The  most  important  of  the  secondary  elements  is  the 
lead  accumulator  or  storage  battery.  If  we  put  two 
lead  electrodes  in  a  solution  of  sulphuric  acid  a  small 
amount  of  PbSCU  is  formed  by  chemical  action  on  the 
surface  of  the  electrodes.  If  we  pass  a  current  through 
the  solution,  the  PbSC>4  on  the  cathode  becomes  reduced 
to  metallic  lead,  and  at  the  anode  is  oxidized  to  lead 
peroxide  (PbO2),  so  that  we  now  have  a  polarization 
element  (cf.  p.  152)  of  the  form 

Pb|H2SO4|PbO2. 

This  can  furnish  a  current  and  has  an  electromotive 
force  of  about  2  volts.  Since  the  formation  of  PbSC>4 
was  very  slight,  very  little  Pb  and  PbO2  was  formed 
and  the  cell  can  only  furnish  a  small  amount  of  electricity. 
To  increase  the  capacity,  i.e.,  to  allow  of  the  formation  of 
large  amounts  of  PbO2,  the  electrodes  should  expose 
as  large  a  surface  as  possible.  This  may  be  accomplished, 
according  to  Plante*,  by  electrolyzing  first  in  one  direction 
and  then  in  the  other,  which  causes  the  electrodes  to 
become  somewhat  porous;  or,  according  to  Faure,  a 
paste  of  lead  oxide  and  red  lead  is  spread  on  a  grating 
of  lead  and  when  this  is  electrolyzed  we  obtain  spongy 


ELECTROMOTIVE  FORCE  AND   GALVANIC  CURRENT.     149 

lead  at  the  cathode  and  lead  peroxide  at  the  anode. 
When  such  an  element  furnishes  a  current  PbSO4  is 
formed  -at  both  electrodes. 

In  "Charging,"  the  PbSO4  on  the  cathode,  or  "  nega- 
tive pole,"  is  reduced  to  Pb,  and  the  following  reaction 
occurs  :  * 


This  is  an  electrode  of  the  second  -kind,  which  sends 
SO  4"  ions  into  solution  (cf.  p.  141).  At  the  anode  or 
"  positive  pole  "  SO4"  ions  are  set  free,  which  through 
the  agency  of  water  ,act  on  the  PbSO4,  forming  PbO2 
and  H2SO4: 


In  "  Discharging,"  SO4"  is  liberated  at  the  anode  (now 
the  lead  pole): 

Pb  +  S04"  +  2©=PbS04. 

At  the  cathode  (now  the  PbO2  pole)  H'  ions  are  dis- 
charged and  with  the  help  of  the  H2SO4  act  on  the  PbO2 
and  convert  it  into  PbSO4: 

PbO2  +  2H"  +  H2SO4  +  2©  =  PbSO4  +  2H2O. 

Summing  up  these  equations  we  obtain  as  the  chemical 
process  which  produces  the  current  the  equation 

PbO2  +  Pb  +  2H2SO4  <=±  2PbSO4  +  2H2O. 

*  In  equations  the  symbol  ©  represents  96  540  coulombs  of  positive 
electricity,  0  the  same  quantity  of  negative 


1 5  °  ELECTROCHEMIS  TR  Y. 

Read  from  right  to  left  this  represents  the  reaction  on 
charging,  from  left  to  right  the  reaction  on  discharging. 
In  charging  2PbSO4  and  2H2O  disappear  and  TbO2, 
Pb,  and  2H2SO4  are  formed;  the  reverse  is  true  on  dis- 
charging.* 

*  On  the  application  of  the  different  thermodynamical  and  electro- 
chemical theories  to  the  lead  accumulator,  see  Book  II,  and  also  the 
excellent  work  of  F.  Dolezalek,  "  The  Theory  of  the  Lead  Accumula- 
or,"  Wiley  &  Sons. 


CHAPTER  VI. 

POLARIZATION  AND   ELECTROLYSIS. 

IN  this  chapter  we  will  discuss  briefly  a  number  of 
facts  which  are  of  the  greatest  importance  to  the  ex- 
perimental and  technical  side  of  electrochemistry  and 
which  will  be  easily  understood  from  what  has  been 
said  in  the  previous  chapters.  The  way  in  which  a 
current  is  conducted  through  a  solution  and  the  part 
played  by  the  different  ions  has  been  discussed  in  the 
chapter  on  conductivity. 

On  arriving  at  the  electrodes  the  ions  give  up  their 
charges,  and  are  either  precipitated  as  neutral  substances, 
where  they  remain  in  a  solid  state  as  in  the  case  of  the 
metals,  or,  as  in  the  case  of  the  gases,  escape  into  the  at- 
mosphere or  dissolve  in  the  solution;  on  the  other  hand, 
they  may  react  at  once  with  the  surrounding  solution  as 
soon  as  they  are  set  free,  and  thus  give  rise  to  oxidizing 
or  reducing  effects.  As  a  result  of  electrolysis  either  the 
electrode  or  the  solution  around  the  electrode  is  changed, 
and  conditions  are  produced  which  result  in  an  electro- 
motive force  opposed  to  that  which  is  sending  the  current 
through  the  solution;  in  other  words,  the  electrolytic  cell 
becomes  "  polarized." 


15*  ELECTROCHEMISTRY. 

Polarization. 

If  we  electrolyze  a  solution  of  HC1  with  an  electro- 
motive force  of  0.7  volt,  a  very  small  quantity  of  hydrogen 
is  deposited  at  the  cathode,  and  a  very  small  quantity 
of  chlorine  at  the  anode,  and  current  will  flow  until  the 
concentrations  of  the  gases  in  the  cell  PtH2  |HCl|PtCi2 
is  high  enough  to  produce  a  counter  electromotive  force 
just  equal  to  the  applied  0.7  volt.  A  hydrogen-chlorine 
cell  in  which  the  gases  have  a  pressure  of  i  atmosphere 
has,  according  to  the  table  on  p.  135,  a  voltage  of  1.35. 
At  o.  7  volt  we  therefore  have  a  H2  —  Cl2  cell  in  which  the 
concentration  of  the  gases  and  therefore  their  solution 
pressure  is  much  smaller  than  at  atmospheric  pressure 
(cf.  p.  136).  These  concentrations  only  become  high 
enough  to  just  balance  the  applied  voltage. 

In  order  to  produce  this  formation  of  H2  and  C12 
current  must  flow  on  applying  an  electromotive  force, 
but  this  soon  stops  on  account  of  the  counter  electro- 
motive force  of  the  H2-C12  cell  which  is  thus  formed. 
If  we  now  increase  the  applied  voltage  to  i  volt  a  new 
current  appears,  the  electrodes  become  charged  with 
more  gas,  and  the  chlorine  hydrogen  cell  also  soon  attains 
an  electromotive  lorce  of  i  volt.  This  goes  on  until  we 
come  to  1.35  volts.  At  this  voltage  the  electrodes  are 
charged  with  gas  at  atmospheric  pressure. 

This  counter  electromotive  force  is  called  "  polariza- 
tion." 

If  we  now  increase  the  voltage  to  1.5  the  polarization 
is  no  longer  able  to  bring  the  current  down  to  zero,  and 
above  1.35  volts  we  have  a  perceptible,  continuous  current. 
1.35  is  called  the  decomposition  voltage  of  HC1.  Above 
1.35  volts  the  current  follows  the  law, 


POLARIZATION  AND  ELECTROLYSIS.  153 

E  —  £  =  iw, 

where  E  is  the  applied  voltage,  e  the  counter  electro- 
motive force  of  polarization,  and  w  the  resistance  of  the 
solution.  The  polarization  increases  very  slightly  above 
1.35  as  the  voltage  and  current  rise,  since  the  gases  are 
evolved  under  a  pressure  greater  than  that  of  the  atmos- 
phere, but  since  they  are  able  to  escape  in  gaseous  form 
the  polarization  will  never  be  as  great  as  the  applied 
electromotive  force. 

Similar  conditions  also  prevail  when  solid  substances 
are  precipitated.  For  instance  when  we  electrolyze  a 
solution  of  CuCl2  between  Pt  electrodes,  chlorine  is 
formed  at  the  anode  under  a  certain  pressure,  and  at  the 
cathode  a  Cu  coating  of  such  a  density  that  the  resulting 
cell 


has  the  same  electromotive  force  as  the  applied  voltage. 

The  small  amount  of  electricity  which  is  necessary 
to  bring  the  electrode  into  the  polarized  condition  is 
known  as  the  "  polarization  capacity  "  of  the  electrode. 
This  capacity  is  naturally  dependent  on  the  surface  of 
the  electrode  and  further  depends  on  the  nature  of  the 
metal  of  which  the  electrode  is  made.  For  equal  surfaces 
palladium  has  a  higher  polarization  ^capacity  when  hy- 
drogen is  discharged  on  it  than  platinum,  and  platinum 
a  higher  capacity  than  iron  ;  for  the  solubility  of  hydrogen 
is  the  greatest  in  palladium,  and  consequently  a  larger 
amount  of  hydrogen  and  therefore  a  larger  amount 
of  current  is  required  to  bring  the  hydrogen  dissolved 
in  palladium  up  to  the  same  pressure  as  that  dissolved 
in  platinum  or  iron. 


154  ELECTROCHEMISTRY. 

If  for  any  reason  the  substances  which  cause  polar- 
ization are  removed,  either  by  dissolving  in  the  solu- 
tion and  diffusing  away,  or  by  chemical  actions,  we  say 
that  "  depolarization  "  occurs.  This  is  the  case  when 
we  electrolyze  a  substance  which  gives  soluble  gases. 
Further,  polarization  is  prevented  when  we  have  a  re- 
ducing agent,  as  FeCl2  at  the  anode,  for  this  prevents 
the  oxygen  polarization  by  combining  with  oxygen  to 
form  a  ferric  salt  (cf.  p.  143).  Such  substances  are 
called  "  depolarizers."  FeCls  is  a  cathodic  depolarizer^ 
since  it  prevents  the  hydrogen  polarization  and  is  reduced 
to  FeCl2. 

The  electrolysis  of  water  furnishes  a  good  illustration 
of  these  facts.  If  we  apply  i  volt  to  two  platinum  elec- 
trodes in  water,  the  cathode  becomes  charged  with  hydro- 
gen and  the  anode  with  oxygen  until  the  electromotive 
force  of  this  gas-cell  is  i  volt,  when  the  current  should 
stop.  The  two  gases  C>2  and  H2,  however,  are  soluble 
in  water,  and  they  consequently  diffuse  away  from  their 
electrodes  and  either  escape  into  the  air  or  recombine 
at  the  electrodes  to  form  water.  The  electrodes  therefore 
are  continually  losing  gas,  and  in  order  to  make  good 
this  loss  and  keep  up  the  electromotive  force  of  i  volt  a 
small  current  must  continue  to  flow.  This  small  current 
is  known  as  the  residual  current  (Reststrom).  Such 
substances  as  are  easily  oxidized  at  the  anode  and  reduced 
at  the  cathode  may  maintain  a  much  larger  residual 
current.  For  instance  if  an  iron  salt  gets  into  the  storage 
battery,  it  is  reduced  to  ferrous  salt  at  the  cathode, 
diffuses  to  the  anode,  and  is  there  oxidized  to  ferric  salt, 
diffuses  back  to  the  cathode,  and  is  again  reduced,  etc. 
Iron  salts  in  the  storage  battery  therefore  maintain  a 


POLARIZATION  AND  ELECTROLYSIS. 


.'55 


residual  current  which  is  useless  for  charging  purposes 
and  causes  a  considerable  loss. 

If  oxygen  or  air  is  passed  over  the  cathode  during 
the  electrolysis  of  water,  this  removes  the  hydrogen 
polarization,  and  such  an  electrode  is  called  "  unpolar- 
izable."  Those  anodes  are  unpolarizable  which  are 
electrolytically  dissolved,  such  as  Cu.  In  general  an 
electrode  is  unpolarizable  when  no  new  substance  is 
formed  on  it  during  electrolysis. 

In  order  to  determine  the  decomposition  voltage  of  a 
salt,  we  put  two  Pt  electrodes  in  the  solution  and  connect 
them  with  a  source  of  electricity  whose  voltage  may  be 


1.3      l.GT] 

FIG.  17. 

varied  at  will.  We  then  gradually  increase  the  voltage 
and  observe  the  current  at  each  voltage.  The  current 
first  rises  and  then  decreases  almost  to  zero  every  time 
the  voltage  is  raised,  until  the  decomposition  voltage 
£  is  reached.  From  this  point  on  the  current  follows 
Ohm's  law  (cf .  p.  78) : 


E  — 


w. 


If  the  voltage  is  plotted   as  abscissa  and  the  current 
as  ordinate  we  obtain  the  curves  shown  in  Fig.  17.    In 


156  ELECTROCHEMISTR  Y. 

the  case  of  AgNO3  the  current  below  0.7  volt  is  prac- 
tically zero,  above  this  it  increases  regularly.  0.7  volt 
is  therefore  the  decomposition  voltage  of  silver  nitrate. 

The  values  in  the  following  table  were  obtained  by 
Le  Blanc  and  his  students. 

DECOMPOSITION  VOLTAGES. 

Acids  Salts 

Sulphuric  acid,  H2SO4 i .  67       Zinc  sulphate,  ZnSO4 2 .35 

Nitric  acid,  HNO3 i .  69      Zinc  bromide,  ZnBr2 i .  80 

Phosphoric  acid,  H3PO4.  ...    1.72       Nickel  sulphate,  NiSO4 2.09 

Malonic  acid',  CH2(COOH)2   i  .69      Nickel  chloride,  NiCl2 i  .85 

Perchloric  acid,  HC1O4 i .  65       Lead  nitrate,  Pb(NO3)2 1.52 

Hydrochloric  acid,  HC1 i  .31       Silver  nitrate,  AgNOs 0.70 

Oxalic  acid °  •  95  Cadmium  nitrate,  Cd(NOs)2  i .  98 

Hydrobromic  acid 0.94  Cadmium  sulphate,  CdSO4  .  2.03 

Hydriodic  acid 0.52  Cadmium  chloride,  CdCl2. . .  i . 88 

Cobalt  sulphate,  CoSO4.  ...  1.92 

Bases  Cobalt  chloride,  CoCl2 i .  78 

Sodium  hydroxide,  NaOH .  .  i .  69 
Potassium  hydroxide,  KOH.  i .  67 
Ammo'm  hydroxide,NH4OH.  i .  74 

Since  the  polarization  is  nothing  less  than  a  gal- 
vanic cell  resulting  from  electrolysis,  it  will  follow  the 
same  laws  and  formulae  as  these  cells.  Just  as  the 
electromotive  force  of  a  galvanic  cell  is  made  up  of  two 
separate  potentials  (cf.  p.  132)  so  the  decomposition 
voltage  of  an  electrolyte  is  composed  of  the  two  voltages 
necessary  to  discharge  the  ions.  Furthermore  these 
"deposition  voltages"  must  be  exactly  the  same  as  the 
single  potentials  of  the  metals  which  are  being  deposited. 
They  also  follow  Nernst's  formula,  i.e.,  the  deposition 
voltage  is  lower,  and  precipitation  takes  place  easier  when 
the  concentration  of  the  ions  which  are  to  be  precipi- 
tated is  high.  The  decomposition  voltage  of  zinc  chlo- 
ride, 2.1  volts,  is  composed  of.  the  potential  of  zinc,  0.77, 
and  that  of  chlorine,  1.35  (cf.  table  on  p.  135).  The 


POLARIZATION  AND  ELECTROLYSIS.  157 

deposition  voltages  may  be  measured  by  combining  the 
electrode  in  question  with  one  whose  potential  i ;  constant 
and  of  known  value.  If  a  current  is  passed  through  the 
combination 

Pt|CuSO4— H2SO4  +  Hg2SO4|Hg 

so  that  Cu  is  precipitated,  it  is  found  that  the  electro- 
motive force  of  the  resulting  cell, 

Cu|CuS04— H2S04  +  Hg2S04|Hg, 

is  0.315  volt.  Knowing  that  the  single  potential  of  the 
mercurous  sulphate  electrode  is  —0.644  (cf.  p.  140) 
we  find  that  the  deposition  voltage  of  Cu  is  -0.329, 
which  is  just  the  same  as  the  single  potential  of  Cu. 

There  is  still  another  kind  of  polarization,  in  which 
the  electrodes  are  not  changed.  If  we  have  two  silver 
electrodes  in  a  solution  of  AgNO3,  and  pass  a  current, 
a  displacement  of  the  concentration  occurs,  due  to  the 
different  velocities  with  which  the  anion  and  cation  move 
(cf.  p.  108).  Consequently  a  concentration  cell  is  formed 
whose  electromotive  force  acts  in  opposition  to  the  applied 
voltage.  This  cell  also,  like  all  concentration  cells, 
must  follow  Nernst's  formula. 

Deposition  and  solution  do  not  necessarily  accompany 
electrolysis.  Other  reactions,  as  oxidation  and  reduction, 
may  take  place,  and  these  obey  the  laws  which  have 
been  discussed  in  the  preceding  pages.  Every  reaction 
taking  place  at  an  electrode  has  its  own  particular  voltage. 
For  instance,  it  requires  a  definite  potential  to  reduce 
FeCl3  to  FeCl2. 

In  certain  cases  the  gases  do  not  act  in  accordance 
with  Nernst's  formula.  When  a  gas  is  evolved  at  an 


158 


ELECTROCHEMISTRY. 


electrode  two  separate  reactions  are  to  be  distinguished: 
first,  the  discharge  of  the  ions  to  form  atoms,  as 


and  secondly,  the  union  of  the  atoms  to  form  the  mole- 
cules of  the  gas,  as 


This  reaction  meets  with  a  different  resistance  from  the 
different  metals  used  as  electrodes,  or,  more  correctly, 
this  reaction  has  a  great  chemical  resistance  which  is 
removed  catalytically  to  a  different  extent  by  the  different 
metals.  Platinized  platinum  is  the  most  effective  cata- 
lyzer for  this  purpose;  hydrogen  is  evolved  on  platinized 
platinum  at  the  potential  o.o  volt.  Iron  is  less  effective 
as  a  catalyzer  and  Hg,  Pb,  and  Zn  are  the  least.  This 
phenomenon  is  called  "  overvoltage,"  and  we  say  that 
hydrogen  is  evolved  on  zinc  with  an  overvoltage  of 
0.7  volt.  The  following  table  shows  the  overvoltages 
necessary  to  evolve  hydrogen  and  oxygen  on  the  different 
metals. 

OVERVOLTAGE. 


Hydrogen  Deposition 

Oxygen  Deposition 

Metal 

Potential 

Metal 

Potential 

Pt  platinized  
Au  
Fe  in  NaOH  
Pt  polished  
As 

o.oo 

O.OI 

0.08 
0.09 
0.15 

0.21 
0.23 
0.46 

o-53 
0.64 

0.70 
0.78 

Au  
Pt  polished  
Pd        

i-75 
1.67 

•65 
•65 
•63 
•53 

.48 

•47 
•47 
•36 
•35 
.28 

Cd  .    . 

As..  . 

N!""  

Pb  

Pn 

Cu 

Pd                 

Fe  

Sn    .  ;  

Pt  platinized.  .    .    . 
Co 

Pb 

Zn  

Ni  polished  
Ni  spongy.     

He.  . 

POLARIZATION  AND  ELECTROLYSIS.  159 

The  recognition  of  these  facts  was  extremely  important, 
for  it  explained  a  number  of  experimental  discoveries 
which  could  not  be  theoretically  accounted  for. 

In  nearly  all  solutions  there  are  several  different  ions 
which  may  be.  discharged,  and  consequently  several 
different  reactions  are  possible  at  the  electrodes.  The 
general  rule  is  that  that  process  actually  takes  place 
which  requires  the  least  expenditure  of  energy.  For 
instance,  if  we  have  a  solution  containing  ZnCl2,  CuCl2, 
and  HC1  no  electrolysis  will  be  effected  by  any  electro- 
motive force  less  than  i  volt,  for  the  decomposition 
voltage  of  CuCl2  is  i  volt.  Between  i  and  1.35  volts 
the  only  reaction  at  the  cathode  will  be  the  deposition 
of  Cu,  since  the  decomposition  voltage  of  HC1  is  1.35. 
Above  1.35  volts  both  Cu  and  H  may  be  deposited,  but 
in  reality  that  process  will  take  place  which  requires  the 
lowest  voltage,  and  only  Cu  will  be  deposited  as  long 
as  it  is  present  in  sufficient  quantity.  If  the  solution 
is  electrolyzed  with  a  high  current,  however,  the  Cu 
in  the  immediate  neighborhood  of  the  cathode  soon 
becomes  nearly  all  used  up,  its  deposition  voltage  is 
raised  in  accordance  with  Nernst's  formula,  and  finally 
a  condition  is  reached  where  hydrogen  is  more  easily 
discharged  than  copper.  Finally,  if  the  voltage  is  raised 
above  2.2  zinc  may  also  be  deposited,  and  this  may  be 
brought  about  by  using  a  high-current  density  so  that 
the  solution  around  the  cathode  contains  very  little 
copper.  By  using  a  high-current  density  brass  may  be 
deposited  on  the  cathode  on  electrolyzing  a  mixture  of 
copper  and  zinc  salts. 

Now,  hydrogen  ions  are  always  present  in  some  quantity, 
and  the  fact  that  zinc  may  be  deposited  from  a  solution 


160  ELECTROCHEMISTRY. 

containing  hydrogen  ions  can  only  be  explained  by  the 
phenomenon  of  overvoltage.  If  there  were  no  over- 
voltage  we  could  no  more  deposit  zinc  from  a  water 
solution  than  we  can  aluminium  or  sodium.  As  it  is 
zinc  can  only  be  precipitated  from  a  neutral  or  alkaline 
solution,  and  not  from  one  containing  acids.  The 
deposition  voltage  of  zinc  is  0.77,  that  of  hydrogen  from 
an  acid  solution,  on  account  of  the  overvoltage,  is  raised 
from  o.o  to  0.70  as  soon  as  the  slightest  trace  of  zinc 
is  deposited.  In  an  acid  solution  the  hydrogen  will 
therefore  be  deposited  before  the  zinc.  In  a  neutral 
solution,  however,  when  the  concentration  of  the  H- 
ions  is  about  io~7  the  deposition  voltage  of  hydrogen 
is  raised,  and  is  0.0577  log  io~7  =  0.404  volt  higher  than 
in  an  acid  solution ;  it  is  raised  still  further  in  an  alkaline 
solution  where  the  H*  ion  concentration  is  very  much 
lower.  From  a  neutral  solution,  therefore,  hydrogen  can 
be  discharged  electrolytically  on  zinc  only  at  a  potential 
of  0.4  +  0.7  =  1.1  volts,  and  consequently  from  such  a 
solution  the  zinc  will  be  deposited  before  the  hydrogen. 

What  is  true  of  the  deposition  of  ions  is  true  of  certain 
other  reactions:  that  one  occurs  first  which  requires  the 
lowest  potential.  If  we  have  a  solution  of  potassium 
permanganate  and  chloric  acid,  that  one  of  these  sub- 
stances will  be  first  reduced  which  has  the  highest  ox- 
idizing potential,  for  oxidizing  potential  is  nothing  less 
than  the  effort  of  the  substance  to  give  up  oxygen  and 
become  reduced.  Such  processes  are  really  nothing  less 
than  a  change  of  the  charges  on  the  ions.  For  instance, 
the  reduction  of  FeCl3  to  FeCl2  simply  consists  in 
Fe'"— >Fe".  The  reduction  of  MnC>4  to  a  manganese 
salt  consists  in  MnO4'— »Mn".  If  we  keep  in  mind  this 


POLARIZATION  AND  ELECTROLYSIS. 


161 


transfer  of  charges,  we  can  derive  a  formula  similar  to 
Nernst's  for  all  such  reactions. 

Using  the  method  explained  on  p.  155  we  can  often 
obtain  the  deposition  voltages  of  every  kind  of  ion  in 
the  solution  (Fig.  18).  In  the 
anodic  curve  for  H2SO4  a 
slight  bend  is  noticed  at  1.12 
volts  where  the  oxygen  ions 
are  discharged.  The  change 
in  direction  of  the  curve  is 
slight,  as  Fig.  18  shows,  be- 
cause the  concentration  of  the 
O"  ions  is  excessively  small, 
and  when  used  up  they  are 
not  immediately  replaced  by 
of  the  water. 


J.1&      1.07  Volt—*. 

FIG.  18. 


a  further  dissociation 
On  further  raising  the  voltage  another 
bend  is  noticed  at  1.67  volts  which  probably  corresponds 
to  the  discharge  of  the  OH'  ions.  Under  suitable  con- 
ditions two  other  points  are  obtained  with  H2SO4,  at 
1.9  where  the  SO4"  ions  are  discharged  and  at  2.6  where 
the  HSO/  ions  are  discharged. 

The  following  deposition  voltages  not  contained  in 
the  other  table  have  been  obtained  by  Nernst  and  his 
students : 

Mg +1.482  SO4 -1.9 

Al +1.276  HS04 -2.6 

*O -i.  12  NO3 -1.88 

*OH -1.67 

*  These  figures  refer  to  solutions  normal  with  respect  to  the  H'  ion;  i.ia 
and  1.67  are  the  deposition  voltages  of  O"  and  OH'  from  a  normal  acid  solu- 
tion. 

To  discharge  OH'  or  O"  ions  from  a  normal  alkaline 
solution  requires  0.8  volt  less  than  to  discharge  them 


1 6  2  ELECT  ROCHE  MIS  TR  Y. 

from  a  normal  acid  solution;  to  discharge  H  from  a 
normal  alkaline  solution  requires  0.8  volt  more  than 
from  a  normal  acid  solution. 

Faraday's  Law. 

As  we  have  already  shown  (pp.  52,  82),  equivalent 
quantities  of  the  ions  of  different  substances  are  always 
combined  with  the  same  amount  of  electricity,  and 
this  charge  is  96  540  coulombs  for  every  equivalent  in 
grams.  This  amount  of  electricity  is  carried  by  39.15 
grams  of  the  positively  charged  univalent  potassium 
ion,  or  by  35.5  grams  of  negatively  charged  univalent 
chlorine  ion.  In  general  the  ions  of  any  substance 
carry  96  540  coulombs  for  every  valence. 

If  one  equivalent  of  any  substance  passes  through 
the  cross-section  of  an  electrolytic  cell,  it  carries  with 
it  96  540  coulombs  and  the  current  strength  is  96  540 
ampere-seconds.  When  108  grams  of  silver  are  de- 
posited on  the  cathode,  96  540  coulombs  of  positive 
electricity  pass  from  the  solution  to  the  electrode.  If 
i  coulomb,  i.e.,  i  ampere  for  i  second,  is  passed  through 
an  electrolytic  cell  0.01036  mg.  equivalents  are  deposited. 
Faraday's  law  may  therefore  be  stated:  The  amount  of 
electricity  required  to  deposit,  dissolve,  or  otherwise  bring 
into  chemical  action  i  gram  equivalent  of  any  element  or 
compound  is  always  p6  540  coulombs.  The  weight  in 
grams  of  the  substance  which  is  produced  or  destroyed 
may  therefore  be  obtained  by  dividing  the  molecular 
weight  (in  the  case  of  elements  the  atomic  weight)  by  the 
valence,  multiplying  by  the  number  of  ampere-seconds 
and  then  by  0.00001036.  The  following  table  contains 
in  the  first  column  the  elements,  in  the  second  the  atomic 


POLARIZATION  AND  ELECTROLYSIS. 


163 


weights,  in  the  third  the  milligrams  per  ampere-second, 
and  in  the  fourth  the  grams  per  ampere-hour.  All  the 
values  except  those  for  H',  Ag",  and  Cu"  are  approxi- 
mate. 


Elements 

Symbol 
and 
Valence 

Atomic 
Weight 

Milligrams 

A    pef 
Ampere- 
second 

Grams  per 
Ampere- 
hour 

A1-" 

27.  1 

o  .  oo  ^  <; 

O   337 

Sb- 

I2O.  2 

0.415 

1  .494 

Sb  

120.2 

0.25 

0.90 

Ba" 

137.4 

0.712 

2  .56 

Bi- 

208.5 

1.  08 

3.89 

Bromine               

Br' 

79.96 

0.8 

2  .Q4 

Cadmium  

Cd" 

II2-4 

0.58^? 

2.  IO 

Calcium     

Ca" 

4O.  I 

o.  207=; 

0.75 

Carbon             

C"" 

12  .OO 

o  031 

o.  1115 

Chlorine     '           

Cl' 

•2C      AC 

o.  ^677 

i    322 

Cobalt                     

Co" 

<q.o 

o  306 

I  .  IO 

Cu" 

6*  6 

o  66 

O    237 

«        (cupiic) 

Cu" 

63  6 

i   186 

Gold  (aurous)  

Au- 

107  •  2 

2    O4.3 

7  36 

"      (auric). 

Au— 

107.  2 

o  68 

2    45 

Hydrogen     •           

H* 

I   008 

o  0104 

o  03762 

Iodine       '                    

I' 

126  85 

i    314. 

A    72^ 

Iron  (ferrous)          

Fe" 

CJC     Q 

O    2OO 

I    O4 

'  '     (ferric)        

Fe'" 

er    o 

O    IQ3 

o  604 

Lead      •                    

Pb" 

jj-y 

2OO   0 

I    O72 

3  86 

Magnesium                  .      ... 

Me" 

24.  36 

o  126 

O    4^3 

Manganese  (manganous).  .  . 
(manganic)  
'  '            (permanganate)  . 
Mercury  (mercurous)  
'  '         (mercuric) 

Mn" 
Mn- 
Mn  
Hg" 

Her" 

55-o 
55-o 
55-° 
200.  o 
200  o 

0.285 

o.  19 

0.08 

2  .072 

1.025 

0.88 
0.29 
7-45 

373 

Nickel 

Ni" 

<8    7 

•  /o 
I    OQ3 

Oxygen  

O" 

50-7 
1  6  oo 

o  083 

o  208^ 

Platinum 

Pt 

iod.  8 

Potassium 

K* 

?Q    I  ^ 

I    46 

Silver 

As' 

IO7    Q'? 

i  118 

A       O2^ 

Sodium   .  .  . 

Na' 

2  ^    O? 

o  86 

Strontium 

Sr" 

*6-  WJ 

87  6 

i  63? 

Sulphur 

S" 

o  ^08 

S"" 

•32    06 

o  083 

o  298 

Tin  (stannous) 

Sn" 

119  o 

2    23 

'  '     (stannic).       .             .  .    . 

Sn"" 

1  19  o 

O    31 

I     II 

Zinc  

Zn" 

5e  A 

I     222 

164  ELECTROCHEMISTRY. 

The  quantity  of  any  substance  formed  or  destroyed  is 
easily  obtained  with  the  help  of  this  table.  For  instance, 
in  the  electrolysis  of  Na2SO4,  H2SO4  is  formed  at-  the 
anode  and  NaOH  at  the -cathode.  The  equivalent  of 
the  first  is  J(i  +  i  +32 +64)  =  49  =  0.507  mg.  of  H2SO4 
per"  ampere-second ;  the  equivalent  of  NaOH  is  23  +  16  +  1 
=  40,  so  that  0.414  mgr.  NaOH  are  formed  per  ampere- 
second.  At  the  same  time  8X0.01036  =  0.0834  mgr.  of 
oxygen  is  liberated  at  the  anode  and  1.01X0.01036  = 
0.0105  mgr.  of  hydrogen  at  the  cathode. 

Electrolysis. 

We  will  now  discuss  briefly  a  few  of  the  most  important 
reactions  which  occur  at  the  electrodes. 

Acids,  and  the  salts  of  all  metals  which  are  discharged 
less  easily  than  hydrogen,  give  off  hydrogen  at  the  cathode 
on  electrolysis,  and  in  the  case  of  these  salts  the  hydroxide 
of  the  metal  is  also  formed.  In  a  solution  of  NaCl  the 
current  is  transported  by  the  ions  Na*  and  Cl',  since  these 
are  present  in  far  greater  quantities  than  the  ions  of 
water,  H*  and  OH'.  The  passage  of  electricity  from 
the  solution  to  the  cathode,  however,  is  taken  care  of, 
not  by  the  Na"  ions,  but  by  the  H'  ions,  since  these  have 
a  much  lower  deposition  voltage.  At  the  cathode,  there- 
fore, H'  ions  disappear  and  pass  off  as  gaseous  H2,  OH' 
ions  remain,  and  Na'  ions  are  brought  up  by  the  current, 
so  that  the  result  of  electrolysis  is  the  formation  of  NaOH 
and  gaseous  H2  at  the  cathode. 

The  concentration  of  the  ions  must  always  be  considered 
as  on  p.  156.  The  deposition  of  nickel  from  an  acid 
solution  is  impossible,  since  from  such  a  solution  H'  ions 


POLARIZATION  AND  ELECTROLYSIS.  165 

are  more  easily  discharged  than  the  Ni"  ions,  but  Ni  can 
easily  be  deposited  from  a  neutral  or  alkaline  solution. 

The  deposition  of  zinc  is  only  made  possible  by  the 
high  overvoltage  of  H  on  zinc.  If  the  zinc  solution 
contains  another  metal  such  as  iron  which  is  easily 
deposited  and  on  which  the  overvoltage  of  hydrogen 
is  not  so  high,  the  least  trace  of  this  metal  on  the  cathode 
gives  the  hydrogen  an  opportunity  to  be  discharged,  and 
no  zinc  can  be  deposited ;  on  the  contrary,  if  any  zinc  has 
been  precipitated  it  redissolves  at  once  with  the  evolution 
of  hydrogen. 

For  similar  reasons  the  presence  of  foreign  metals  in  a 
storage  battery  is  very  injurious.  The  reduction  of 
PbSCU  at  the  cathode  would  be  impossible  if  lead  showed 
no  overvoltage.  As  a  matter  of  fact,  when  we  try  to  re- 
duce PbSC>4  on  a  Pt  electrode  no  lead  is  formed,  and  we 
have  simply  an  evolution  of  hydrogen.  The  same  thing 
happens  when  a  foreign  metal  such  as  copper  gets  into 
the  storage  battery.  It  is  deposited  on  the  cathode,  and 
when  we  attempt  to  charge  the  battery,  hydrogen  is 
evolved  on  the  traces  of  copper  and  no  PbSC>4  is  reduced. 

These  facts  are  important  in  the  analytical  determina- 
tion of  the  metals  by  electrolysis  (cf.  Book  II).  The 
metals  can  only  be  deposited  when  their  deposition 
voltage  is  below  that  of  hydrogen,  and  we  must  give  the 
solution  such  a  composition  that  this 'will  be  the  case. 
In  determining  nickel,  for  instance,  we  use  an  ammo- 
niacal  solution. 

What  has  been  said  also  applies  to  the  reaction  at  the 
anode.  An  anion  will  only  be  discharged  when  this 
reaction  takes  place  easier  than  the  discharge  of  the  O" 
or  OH'  ions  which  are  always  present.  We  can  never 


1 6  6  ELECTROCHEM1S  TR  Y. 

obtain  fluorine  by  electrolyzing  a  water  solution,  but  we 
can  obtain  bromine  and  iodine.  When  we  electrolyze  a 
solution  of  Na2SO4,  the  SO4"  ions  are  not  discharged, 
but  rather  the  oxygen  ions,  and  gaseous  oxygen  is  evolved. 
As  the  oxygen  ions  disappear  hydrogen  ions  remain  in 
the  solution,  and  since  SO4"  ions  are  brought  up  by  the 
current,  this  results  in  the  formation  of  sulphuric  acid  at 
the  anode.* 

Another  class  of  reactions  may  occur  when  the  ions 
which  have  been  brought  up  to  the  anode  find  an  oppor- 
tunity to  enter  into  a  reaction  which  requires  a  potential 
lower  than  that  necessary  for  their  discharge.  In  a 
strongly  acid  solution  of  Na2SO4  which  contains  very 
few  O"  ions,  the  reaction  SO4  +  SO4  =  S2O8  can  be  more 
easily  brought  about  than  the  evolution  of  oxygen, 
consequently  H2S2Os  is  formed  and  little  or  no  oxygen 
is  produced.  In  an  acid  solution  of  Na2SO4,  however, 
OH'  and  HSO4'  ions  are  also  present,  and  it  is  very 
probable  that  the  formation  of  persulphuric  acid  is  due 
to  the  direct  union  of  two  discharged  HSO4  ions. 

We  have  still  to  consider  the  presence  of  OH'  ions. 
When  we  electrolyze  a  solution  with  a  voltage  of  about 
1. 12  or  a  little  higher,  O"  ions  are  discharged,  but  they 
soon  become  so  largely  removed  in  the  vicinity  of  the 

*  It  should  be  noticed  that  many  text -books  explain  these  facts  in  a 
somewhat  different  way,  by  assuming  that  the  SO/'  ions  are  actually 
discharged  and  then  react  with  water  according  to  the  equation 

S04  +  H20=H2S04  +  0. 

The  formation  of  NaOH  at  the  cathode  is  similarly  explained  on  the 
assumption  that  Na  ions  are  first  discharged  and  then  immediately 
react  with  the  water,  forming  H  and  NaOH.  It  is  evidently  unneces- 
sary to  explain  the  facts  in  this  roundabout  way. 


POLARIZATION  AND  ELECTROLYSIS.  167 

electrode  that  their  deposition  voltage  is  raised  above 
that  of  the  OH'  ions.  Therefore  in  the  electrolysis  of 
a  NaOH  solution  we  have  only  a  very  weak  current 
between  1.12  and  1.67  volts.  Above  this  last  voltage, 
which  is  the  deposition  potential  of  the  OH'  ions,  we 
obtain  a  much  stronger  current.  The  reaction  which 
takes  place  at  the  electrodes  is 

OH+OH=H20+O. 

A  reaction  of  this  sort  in  which  the  ions  are  destroyed  is 
evidently  not  reversible  (cf.  p.  12  and  123),  for  the  OH 
ions  cannot  be  restored  to  the  solution  by  reversing  the 
current. 

A  chemical  reaction  may  be  brought  about  more 
easily  than  by  direct  deposition  if  the  ions  have  an  oppor- 
tunity to  form  a  compound  or  alloy.  For  instance,  if  we 
electrolyze  a  sodium  chloride  solution,  using  a  mercury 
cathode,  two  causes  unite  to  lower  the  deposition  voltage 
of  the  Na*  ions  below  that  of  hydrogen:  first,  the  discharge 
of  Na  is  facilitated  because  it  may  unite  with  mercury 
to  form  an  amalgam,  and .  secondly,  the  discharge  of  H 
on  mercury  requires  a  high  overvoltage.  In  this  case 
Na'  ions  can  be  discharged  before  H*  ions,  and  this  fact 
forms  the  basis  of  a  very  important  industry:  the  manu- 
facture of  sodium  amalgam  and  its  subsequent  conversion 
into  pure  sodium  hydroxide. 

These  primary  reactions  of  deposition  are  to  be  dis- 
tinguished (Book  III)  from  secondary  reactions  into 
which  the  deposited  substances  may  enter.  In  the 
electrolysis  of  sodium  chloride  the  chlorine  set  free  at 
the  anode  dissolves  in  the  solution,  diffuses  away,  and 


1 68  ELBCTROCHEM1STR  Y. 

reacts  with  the  NaOH  which  is  formed  at  the  cathode, 
thus: 

2NaOH  +  C12  =  NaOCl  +  NaCl  +  H2O ; 

i.e.,  the  hypochlorite  is  a  secondary  product  of  electrolysis. 
This  reaction  also  has  great  technical  importance,  for  the 
electrolytic  hypochlorite  solutions  are  largely  employed 
for  bleaching  purposes.  If  these  bleaching  solutions  are 
again  electrolyzed  the  hypochlorite  is  oxidized  to  chlorate. 


CHAPTER  VII. 

THE  ELECTRON  THEORY. 

RECENT  researches  on  the  chemical  effect  of  the  silent 
electric  discharge,  on  the  cathode  and  X-rays,  and  es- 
pecially the  discoveries  in  connection  with  radioactivity 
have  caused  the  revival  of  an  old  theory,  according  to 
which  electricity  is  an  actual  chemical  substance  (formerly 
called  the  "  electric  fluid  ").  We  must  confine  ourselves 
to  a  very  brief  outline  of  the  development  of  the  "  electron 
theory  "  and  its  application  to  electrochemical  questions. 

The  cathode  rays  discovered  by  Hittorf  are  rays  sent 
out  from  the  cathode  of  a  vacuum  tube  under  the  in- 
fluence of  very  high  voltages.  They  consist  of  negative 
electricity  which  is  ejected  from  the  cathode  at  a  very 
high  velocity.  These  particles  of  electricity  must  possess 
a  certain  weight,  since  they  are  capable  of  exerting 
a  force  when  in  motion.  At  discharge  potentials  of 
3000  to  14  ooo  volts  their  velocity  ranges  from  0.3  to 
o.yXio10  centimetres  per  second,  i.e.,  is  from  TV  to  J  of 
the  velocity  of  light.  When  the  rays  enter  an  electric 
or  magnetic  field,  their  path  becomes  changed.  From 
this  deviation  and  from  the  velocity  it  has  been  calculated 
that  the  weight  of  the  electric  atom  or  "  electron  "  is 

about  ToW  tnat  °f  tne  hydrogen  atom. 

169 


170  ELECTROCHEMISTRY. 

The  Becquerel  rays  emitted  by  radium  and  other 
radioactive  substances  are  very  similar  to  the  cathode 
rays,  only  their  velocity  (and  consequently,  their  pene- 
trating power)  is  greater,  being  from  2.5  to  2.8Xio10 
cms.  per  second,  or  nearly  as  high  as  the  velocity  of 
light.  If  the  cathode  rays  consist  of  negative  electrons, 
we  must  assume  that  the  same  is  true  of  the  radium 
rays.  It  therefore  follows  that  negative  electrons  are 
capable  of  existing  in  a  free  state  and  not  combined  with 
matter.  The  same  should  be  true  of  the  positive  electrons, 
although  it  is  doubtful  whether  they  have  yet  been  isolated. 

When  electrons  pass  through  air,  they  attach  themselves 
to  the  gas  molecules  and  form  air  ions,  and  the  gas 
becomes  a  conductor  of  electricity.  The  velocities  of 
these  ions  have  been  measured,  and  it  has  also  been 
found  that  they  obey  the  ordinary  laws  of  diffusion. 
The  diffusion  coefficients  of  the  gas  ions  have  been  cal- 
culated on  the  assumption  that  they  are  electrically 
univalent,  i.e.,  contain  only  one  positive  or  negative 
electron,  and  the  calculated  and  experimental  values 
agree  very  well.  The  conductivity  imparted  to  air  by 
the  electrons,  and  also  their  effect  in  causing  the  con- 
densation of  supersaturated  vapors  (which  last  may  also 
be  brought  about  by  dust  particles),  forms  an  important 
test  for  the  presence  of  electrons. 

When  an  electron  moving  at  a  high  velocity  collides 
with  a  "  neutron,"  the  latter  is  broken  up  and  new  positive 
and  negative  electrons  are  formed.  These  may  later  on 
recombine  and  again  form  neutrons,  according  to  the 
equation 


We  must  assume   the  existence   of  these  neutrons  if 


THE  ELECTRON   THEORY.  17* 

we  accept  the  electron  theory.  Neutrons  must  be  present 
everywhere  like  the  ether,  and  are  without  mass,  non- 
conducting but  capable  of  being  polarized.* 

The  following  electrochemical  definitions  would  follow 
from  the  theory.  The  electron  acts  chemically  like 
an  element.  It  combines  with  other  elements  to  form 
saturated  compounds,  which  are  the  ions.  96  540 
coulombs  correspond  to  i  mol  of  a  univalent  element; 
the  ©  unites  with  negative  elements  or  radicals  to  form 
saturated  compounds,  as 


O" 


=  SO4", 


©  can  replace  the  metallic  element  in  compounds,  while 
©  combines  with  the  positive  elements  and  radicals  and 
is  capable  of  replacing  the  negative  elements  and  radicals: 


10 

'fa 


NH4+©=NH4©=NH4-, 


etc. 


If  an  electron  can  spring  from  one  atom  to  another 
as  in  the  reaction 


*  For  further  details  see   Nernst,  Theoretische  Chemie,  4th  edition, 
D.  389  ff. 


172  ELECTROCHEMISTRY. 

it  must  be  capable  of  existing  in  a  free  state  for  a  certain 
length  of  time,  a  conclusion  which  we  have  already  drawn 
from  the  conduct  of  the  cathode  rays. 

The  electrons  have  a  different  affinity  for  the  different 
elements,  just  as  the  elements  have  a  different  affinity 
for  one  another.  The  positive  electrons  have  a  greater 
affinity  for  the  metals,  and  the  order  of  this  affinity  is 
shown  in  the  table  'of  potentials  (p.  135);  the  negative 
electrons  have  an  affinity  for  the  metalloids  and  negative 
radicals.  The  affinity  of  the  positive  electron  ©  for 
any  element  or  radical  increases  as  the  affinity  of  the 
negative  electron  decreases,  as  in  the  following  list: 

F,  S04,  Cl,  O,  Br,  I,  Ag,  Hg,  Cu,  Fe,  Zn,  Al,  Na,  Cs. 

When  two  ions  unite,  as  H'  +  C1'=HC1,  the  molecule 
HC1  is  to  be  considered  as  a  double  salt  of  the  form 
H©QC1,  which  decomposes  into  its  components  on  being 
dissolved  in  H2O: 


i.e.,  it  dissociates  just  as  the  alums  do  when  dissolved: 


These  "  neutron  double  salts  "  in  no  way  resemble 
their  components,  while  the  alloys,  and  compounds  like 
PCla,  BrCl,  etc.,  which  are  not  neutron  double  salts, 
retain  some  of  the  characteristics  of  the  elements  from 
which  they  are  made. 


LITERATURE. 


A.  BOOKS. 

W.   NERNST.      Theoretische   Chemie.     Verlag  von   Enke,   Stuttgart. 

1904. 
Theoretical  Chemistry  from  the  Standpoint  of  Avogadro's  Rule, 

and  Thermodynamics.     Revised  edition.     1904. 
W.  OSTWALD.     Lehrbuch  der  allgemeinen  Chemie.     Verlag  von  En- 

gelmann,  Leipzig      1890-1904. 
Grundriss    der    allgemeinen    Chemie.     Verlag   von   Engelmann, 

Leipzig.     1899. 

The  Scientific  Foundations  of  Analytical  Chemistry.     1899. 

Elektrochemie,  ihre  Geschichte  und  Lehre.    Verlag  von  Veit  & 

Co.,  Leipzig.     1896. 
—  und   R.   LUTHER.     Physico-chemische   Messungen.     Verlag  von 

Engelmann,  Leipzig.     1902. 
A    Manual    of    Physical    and    Chemical    Measurements. 

Macmillan  &  Co.     1902. 
J.  H.  VAN'T  HOFF.     Vorlesungen  iiber  theoretische  und  physikalische 

Chemie.     Verlag  von  Vieweg  &  Sohn,  Braunschweig.     1904. 
Lectures  on  Theoretical  and  Physical  Chemistry.     3  vols.     Long- 
mans, Green  &  Co. 
J.  WALKER.     Introduction  to  Physical  Chemistry.     Macmillan  &  Co., 

New  York. 

W.  RAMSAY.     Modern  Chemistry.     Macmillan  &  Cc. 
W.  NERNST  and  A.  SCHONFLIES.     2  vols.     Einflihrung  in  die  mathe- 

matische  Behandlung  der  Naturwissenschaften.     Verlag  von  Olden- 

bourg,  Miinchen-Berlin.     1904. 
F.  KOHLRAUSCH.      Lehrbuch  der  praktischen  Physik.     Verlag  von 

Teubner,  Leipzig.     1905. 

173 


174  LITERATURE. 

A.  A.  NOYES.     General  Principles  of  Physical  Science.     Henry  Holt  & 

Co.,  New  York.     1902. 
S.   ARRHENIUS.      Lehrbuch  der  Electrochemie.      Verlag  von   Quandt 

&  Handel,  Leipzig.     1901. 

Electrochemistry.     Longmans,  Green,  &  Co. 

M.   LE  BLANC.      Lehrbuch  der  Electrochemie.      Verlag  von  Leiner, 

Leipzig.     1903. 
Elements  of  Electrochemistry.     (A  new  edition  preparing.)     Mac- 

millan  &  Co. 
F.  HABER  .  Grundriss  der  technischen  Elektrochemie  auf  theoretischer 

Grundlage.     Verlag  von  Oldenbourg,  Miinchen.     1898. 
R.    LJBKE.     Grundz'jge    der    Elektrochemie.     Verlag    von    Springer, 

Berlin.     1903. 
P.  TH.  MULLER.     Lois  fondamentales  de    Pelectrochimie.     Masson   & 

Cie,  Paris.     1903. 
A.   HOLLARD.     La  theorie  des  ions    et    Pelectrolyse.     Carre    &   Cie, 

Paris.     1900. 
R.  ABEGG.      Die  Theorie  der   elecktrolytischen  Dissociation.      Verlag 

von  Enke,  Stuttgart.     1903. 

The  Theory  of  Electrolytic  Dissociation.     Wiley  &  Sons. 

H.  C.  JONES.     Theory  of  Electrolytic  Dissociation.     Macmillan  &  Co., 

New  York. 
F.    B.    AHRENS.     Handbuch  der  Elektrochemie.     Verlag    von    Enke, 

Stuttgart.     1903. 
W.  BORCHERS.     Handbuch    der    Elektrochemie.     Verlag  von  Knapp, 

Halle.     (In  preparation.) 

• Elektrometallurgie.     Verlag     v'on     Hirzel,     Leipzig.     1905. 

Electro  Smelting.     Lippincott  Co. 

H.   DANNEEL.     Spezielle  Elektrochemie.     Verlag   von   Knapp,   Halle. 

(In  preparation.) 
Jahrbuch  der  Elektrochemie.     Verlag  von  Knapp,  Halle.     1902- 

1905. 
F.  KOHLRAUSCH  und  L.  HOLBORN.     Das  Leitvermogen  der  Elektro- 

lyte.     Verlag  von  Teubner,  Leipzig.     1898. 

Introduction  to  Physical  Measurements.     Macmillan  &  Co. 

F.    DOLEZALEK.      Die   Theorie   des    Bleiakkumulators.      Verlag   von 

Knapp,  Halle.     1901. 

The  Theory  of  the  Lead  Accumulator.     Wiley  &  Sons. 

F.  M.  PERKIN.     Practical  Methods  of  Electrochemistry.     Longmans, 

Green  &  Co.,  New  York  and  London.     1905. 
R.  LORENZ.     Elektrochemisches  Praktikum.     Verlag  von  Vandenhock 

und  Ruprechht,  Gottingen.     1901. 


LITERATURE.  175 

M.  ROLOFF  und  P.  BERKITZ.     Elektrotechnisches  und  elektrochemisches 

Seminar.     Verlag  von  Enke,  Stuttgart.     1904. 
W.  NERNST  und  W.  BORCHERS.     Jahrbuch  der  Elektrochemie.    Verlag 

von  Knapp,  Halle.     1894-1901. 

B.    PERIODICALS. 

Zeitschrift  fiir  Elektrochemie.     Organ  der   Bunsengesellschaft,  Knapp, 

Halle. 

Zeitschrift  fur  physikalische  Chemie.     Engelmann,  Leipzig. 
Zeitschrift  fur  anorganische  Chemie.     Voss,  Hamburg. 
Journal  of  Physical  Chemistry.     Ithaca,  N.  Y. 

Journal  de  chimie  physique,  Kundig,  Genf;  Gautiers-Villard,  Paris. 
Transactions  of  the  American  Electrochemical  Society.     Published  by 

the  Society,  Philadelphia. 

Electrochemical  Industry.     Electrochemical  Publishing  Co.,  New  York. 
Transactions  of  the  Faraday  Society.     Published  by  the  Society,  London. 


INDEX. 


Absolute  potential,  135 

Absolute  temperature,  10 

Absolute  velocities  of  the  ions,  112 

Absorption  law,  136 

Acceleration,  2 

Accumulator,  147 

Acetic  acid,  dissociation  of,  100 

Acid-alkali  cell,  72,  146 

Acids  and  bases,  strength  of,  97 

Active  mass,  36,  40 

Additive  properties  of  the  ions,  74 

Affinity  of  acids,  102 

Air  pressure,  16 

Air  ions,  170 

Alcohols  as  solvents,  93 

Alloys,  potential  of,  140 

Amalgams,  potential  of,  14 

formation  of,  167 
Ammonia  as  a  solvent,  93 
Ampere,  3,  6 
Analysis,  electrolytic,  165 

and  the  dissociation  theory,  105 
Anion,  51 

Arrhenius,  theory  of,  56 
Atmosphere,  pressure  of,  19 
Atomic  weights,  table  of,  163 
Avogadro's  Law,  18 


Bases,  64 

Bases  and  acids,  strength  of, 
Becquerel  rays,  1 70 
Berthelot's  Principle,  9 
Bleaching  solutions,  168 


97 


Boiling-point,  rise  of,  28,  47 
molecular  rise  of,  47 

Carbon  monoxide  and  oxygen,  38,  41 
Carbon  dioxide,  dissociation  of,  38, 

41 
Calcium  carbonate,  dissociation  of, 

40 

Calomel  electrode,  141 
Calorie,  4 
Capacity,  117 

of  the  storage  battery,  148 
Capillarity,  75 
Catalyzers,  15 
Catalysis  and  dissociation  constant, 

98 

Cataphoresis,  119 
Cathode  rays,  169 
Cation,  51 
Cell,  galvanic,  120 
Chemical  energy,  5,  6 
Chemical  equilibrium,  32 
Chemical-force  and  reaction  velocity, 

14 

Chemcial  kinetics  and  statics,  35,  36 

Chemical  resistance,  15 

Chemical  work  and  osmotic  pressure, 
29 

Chemistry,  applications  of  the  disso- 
ciation theory  in,  61 

Chlorates,  168 

Chlorine  electrode,  138 

Chlorine-hydrogen  cell,  152 
177 


i78 


INDEX. 


Chlorine  potential  of  chlorides.  141 
Clausius,  theory  of,  55 
Complete  reactions,  32 
Compounds,  potential  of,  140 
Concentration  cells  with  respect  to 

the  electrodes,  137,  138 
Concentration  cells  with  respect  to 

the  electrolyte,  144 
Conduction  through  salts,  45 
Conductivity,  77 
Conductivity,  of  acetic  acid,  100 

metallic  and  electrolytic,  80 

of  the  metals,  79 

of  pure  substances,  91 

of  solutions,  8 1 

specific,  78 

temperature  coefficient  of,  79,  107 

of  water,  73 

Conservation  of  energy,  7 
Contact  electricity,  118 
Copper,  precipitation  of ,  by  zinc,  126 
Coulomb,  3,  78 

and  ion,  52 

Current,  production  of,  by  chemical 
means,  115 

Daniell  cell,  n,  121,  126 
Decomposition  voltage,  152,  155,  156 
Depolarization,  154 
Deposition  voltage  of  the  ions,  156, 

160,  161 
Dielectric  constant,  113 

and  dissociating  power,  93,  94 
Diffusion  potential  145 
Dilution  law,  Ostwald's,  101 
Dissociating  power,  92 
Dissociation  constant,  58,  99 
Dissociation  constants,  table  of,  102 
Dissociation  constant  and  hydroly- 
sis, 68 
Dissociation,  electrolytic,  48 

decrease  of,  102 

degree  of,  48,  57,  87 

formula  of  salts,  58 

of  gases,  38 

heat  of,  67 

pressure,  41 

of  salts,  96 

stepwise,  63,  106 

theory  of,  45 

of  water,  73,  147 


Dyne,  2 

Electric  work,  3,  6 
Electricity,    a    chemical    substance, 
169 

quantity  of,  3 
Electrochemistry,  history  of,  49 

and  work  obtainable  from  reac- 
tions, 12 
Electrodes,  51 

of  first  and  second  kind,  141,  142 
Electrolysis,  164 
Electrolyte,  51 

Electrolytic   solution    pressure,    127 
Electrolytic  potential,  130 
Electromotive  force,  calculation  of, 

123 
Electron,  velocity  and  mass  of,  169 

theory,  169 
Element,  120 
Endosmosis,  119 
Energy,  chemical,  5,  6 

electric,  3,  6 

free,  u 

heat,  4 

kinds  of,  i,  6 

kinetic,  7 

law  of  the  conservation  of,  7 

law  of  the  transformation  of,  9 

mechanical,  2 

potential,  8 

radiant,  5 

table  of  equivalents,  5 

temperature  coefficient  of,  10 

volume,  2 

Energy    equation    of    Gibbs-Helm- 
holtz,  124 

of  van't  Hoff,  31,  124 

of  Nernst,  127 
Equilibrium,  chemical,  32 

and  temperature,  41 
Equilibrium,  constant,  35 

concentration,  125 
Equivalent,  83 

conductivity,  83,  86,  90 

weights  table  of,  163 
Ester  formation,  32,  36 
Expansion,  work  done  in,  4 

Faraday's  law,  52,  162 
Ferrocyanide  of  copper  membrane,  24 


INDEX. 


179 


Fluid,  electric,  169 
Force,  5 

chemical,  and    reaction    velocity, 

14 

Free  energy,  n 
Freezing-point,  lowering  of,  27 

molecular  lowering  of,  46 
Friction,  of  the  ions,  93 

internal,  75 

Frictional  electricity,  119 
Fugacity,  127 

Galvani's  experiments,  120 
Galvanic  cell,  120 
Gas-constant  R,  18 

value  of,  in  different  units,  5 
Gas  electrodes,  136 
Gas  laws,  16 
Gas  pressure,  16 
Gases,  dissociation  of,  37 

expansion  of,  2 

work  obtainable  from,  16,  21 

overvoltage  of,  158 
Gay-Lussac's  Law,  16 
Gibbs-Helmholtz  formula,  124 
Gram  equivalent  and  molecule.  18, 

83 

Grottnus,  theory  of,  53 
Grove,  theory  of,  54 
gas  cell,  138,  144 

Heat  energy,  4,  6 

Heat,  mechanical  equivalent  of,  4 

theory  of,  7,  9 
Heat  and  motion,  8 

of  reaction,  8,  43,  44 

of  neutralization,  66 
Helmholtz's  energy  equation,  124 
Henry's  absorption  law,  136 
Heterogeneous  systems,  39 
H.ttorf's  experiments  on  the  trans- 
port number,  55 
Van't  Hoff ,  energy  equation,  31 

laws  of  solutions,  56 

laws  of  dilution,  101 
Homogeneous  systems,  39 
Hydrogen,  deposition  of,  160 

electrode,  133,  137 

electrolytic  potential,  133 

overvoltage  of,  158 
Hvdroiodic  acid,  formation  of,  37 


Hydrolysis,  68 

and  the  dissociation  constant,  71 
Hydroxyl  ions,  deposition  of,  167 
Hypochlorites,  168 

I,  van't  Hoff 's  factor,  table,  49 
Incomplete  reactions,  32,  33 
Insulators,  conductivity  of,  79 
Inversion  of  sugar,  98 
Ions,. -48,  52 

additive  properties  of,  75 

charges  on,  49,  52 

deposition  voltage  of,    156,    160, 
161 

as  electron  compounds,  171 

friction  overcome  by,  113 

reactions  of,  61 

velocities  of,  84 

velocities  of  absolute,  112 
Isohydric  solutions,  103 
Isosmotic  and  isotomic  solutions,  23 

Kinetics,  law  of  chemical,  35 
Kohlrausch,  law  of  the  independent 
wandering  of  the  ions,  5  5 ,  85 , 1 1 1 

Lead,  deposition  of,  165 

storage  battery,  147 
Light,  absorption  of,  75 
Litre  atmosphere,  2,  19 
Liquids,  contact  potential  of,  145 

Mass,  2 

Mass  action,  36,  40 

law  of,  35 

and  dissociation,  57 
Maximum  work,  6,  8 

determination  of,  12 
Mechanical  energy,  2 
Mechanicat  equivalent  of  heat,  4 
Mercury,     potential     and     surface 
tension  of,  135 

normal  electrode,  134 
Metal  solutions,  potential  of,  140 
Metals,  specific  conductivity  of,  79 
Mixtures,  potential  of,  140 
Mol,  18 

Molecule,  gaseous,  18 
Molecular  concentration,  23 
Molecular  conductivity  of  the  ions, 
85 


i8o 


INDEX. 


Nernst's  formula,  127 
applications  of,  146 
Neutralization,  66 
Neutralization  cell,  146 
Neutralization,  heat  of,  66 
Neutron,  170 
Nitrogen,  density  of,  18 
"Nobility"  of  the  metals,  134 
Normal  electrodes,  134,  142 

Ohm's  law,  78,  117 
Osmotic  cells,  25 
Osmotic  work,  30 
Osmotic  pressure,  27 

of  salts,  49 

of  sugar  (table),  26 

and  solution  pressure,  128 

and  work,  20 

Ostwald's  dilution  law,  101 
Oxidation  potential,  143 
Oxygen  electrode,  138 
Oxygen,  overvoltage  of,  158 
Oxygen  and  carbon  monoxide,  38,  41 
Oxygen-hydrogen  cell,  138 

Partial  pressure,  17 

Perpetual  motion,  7,  9 

Persulphuric  acid,  166 

Plant  cells,  osmotic  pressure  of,  22, 

24 
Phosphorous  chloride,  formation  of, 

38 
Physiological  solutions,  76 

Physiology  and  the  theory  of  elec- 
trolytic dissociation,  75 
Plasmolysis,  23 

Platinum  as  semipermeable   mem- 
brane, 25 
Platinum  black,  catalytic  action  of, 

.  136 

Poisonous  action  of  the  ions,  76 
Polarization,  152 

capacity,  153 
Polymerization      and      dissociating 

power,  95 
Potential,  absolute,  135 

of  alloys,  140 

of  compounds,  140 

at  contact  of  solutions,  145 

difference  of,  2,  77,  116 

electric,  116 


Potential,  electrolytic,  130,  134 
energy,  7 
fall  of,  116 
of  mixtures,  140 
of  reducing  and  oxidizing  agents 

143 
Pressure,  2 

osmotic,  and  chemical  work,  30 
Principe  du  travail  maximum,  9 
Principles  of  thermodynamics,  6,  9, 

10 

R,  the  gas-constant,  18 

Radium,  170 

Reaction,  complete  and  incomplete, 

32 

heat  of,  8 

reversible,  34 

work  obtainable  from,  12 
Reaction  velocity,  14,  35 
Reduction  potential,  143 
Residual  current,  154 
Resistance,  chemical,  15 

specific,  of  metals,  79 
Reversibility,  12,  123 

Saponification,  71,  99 

Salt  solution,  osmotic  pressure  of,  47 

Salts,  dissociation  of,  58 

solution  of,  40 
Schlieren  apparat,  28 
Secondary  reactions,  167 
Secondary  elements,  147 
Semipermeable  membranes,  22 

of  Cu2Fe(CN)c,  24 

of  air,  28 

of  ice,  27 

of  platinum,  25 

Series  of  the  elements  according  to 
their  electrolytic  solution  pres- 
sure, 135 
Silver  analysis,  and  the  dissociation 

theory,  104 
Silver,  equivalent    of,    3.     Cf.  also 

Faraday's  law 

Silver  iodide,  solubility  of,  146 
Silver    ions,     precipitation    of,    by 

chlorine  ions,  61 

Sodium  acetate,  hydrolysis  of,  68 
Sodium  amalgam,  167 
Solids,  active  mass  of,  36,  40 


INDEX. 


181 


Solubility,  constant,  40 

from  electromotive  force,  146 
Solubility  product,  104 
Solutions,  conductivity  of,  81 

dilute  and  the  gas  laws,  20 

isotonic,  23 

of  salts,  osmotic  pressure,  47 
Solution  pressure,  electrolytic,  127, 

128 
Solvent,  active  mass  of,  36 

dissociating,  92 
Specific  conductivity  of  metals,  79 


Statics,  law  of  chemical,  35 

Cf. 
ciation 


Stepwise  dissociation.      Cf.    Disso- 


Succinic  acid,  solution  of,  44 
Sugar,  osmotic  pressure  of,  25 

inversion  of,  98 

Sulphuric  acid,  specific  conductivity 
of,  91 

decomposition  voltages  of,  161 

Temperature,  absolute,  10 
and  chemical  equilibrium,  41 

Temperature  coefficient  of  capacity 

for  work,  10 
of  conductivity,  79,  80,  107 

Thomson's  Rule,  9 

Transformation  of  energy,  9 

Transport  number,  108 

Valence,   variable  and  dissociating 
power,  95 


Vapor  pressure  of  water,  41 
lowering  of,  27,  47 

Velocity  of  the  ions,  85 

Volt,  4 

Voltage,  3,  6 

measurement  of,  118 
of  decomposition,  152 

Voltaic  pile,  121 


Walls,  semipermeable,  22 
Wandering  of  the  ions,  law  of  the 

independent,  85 
Water,  conductivity  of,  90 

dissociating  power  of,  93 

dissociation  of,  65,  73,  147 

electrolysis  of,  154 

evaporation  of,  32 

vapor  pressure  of,  41 
Watt  second,  3,  6 
Weight,  2 

Williamson,  theory  of,  55 
Work,  chemical,  and  osmotic  pres- 
sure, 30 

from  expansion  of  gases,  16,  19 

maximum,  7,  9 

from  natural  processes,  6 

osmotic,  19 


Zero,  absolute,  of  temperature,  10 

Zinc,  deposition  of,  160 

Zinc  amalgam,  potential  of,  139 


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Bernadou's  Smokeless  Powder,  Nitro-cellulose,  and  the  Theory  of  the  Cellulose 

Molecule i2mo,  2  50 

*  Bruff's  Text-book  Ordnance  and  Gunnery 8vo,  6  oo 

Chase's  Screw  Propellers  and  Marine  Propulsion 8vo,  3  oo 

Cloke's  Gunner's  Examiner 8vo,  i  50 

Craig's  Azimuth 4to,  3  50 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

Sheep,  7  50 

De  Brack's  Cavalry  Outposts  Duties.     (Carr.) 24mo,  morocco,  2  oo 

Dietz's  Soldier's  First  Aid  Handbook i6mo,  morocco,  i  25 

*  Dredge's  Modern  French  Artillery 4to,  half  morocco,  15  oo 

Durand's  Resistance  and  Propulsion  of  Ships 8vo,  5  oo 

*  Dyer's  Handbook  of  Light  Artillery iamo,  3  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

*  Fiebeger's  Text-book  on  Field  Fortification Small  8vo,  2  oo 

Hamilton's  The  Gunner's  Catechism i8mo,  x  oo 

*  Heff'B  filnatatary  Naval  Tactics. ......................I. > » ,8vo,  i  50 

I 


Ingalls's  Handbook  of  Problems  in  Direct  Fire 8vo,  4  oo 

*  Ballistic  Tables 8vo,  I  50 

*  Lyons's  Treatise  on  Electromagnetic  Phenomena.  Vols.  I.  and  II.  .8vo,  each,  6  oo 

*  Mahan's  Permanent  Fortifications.    (Mercur.) 8vo,  half  morocco,  7  SO 

Manual  for  Courts-martial i6mo,  morocco,  i  50 

*  Mercur's  Attack  of  Fortified  Places i2mo,  2  oo 

*  Elements  of  the  Art  of  War 8vo,  4  oo 

Metcalf's  Cost  of  Manufactures — And  the  Administration  of  Workshops.  .8vo,  5  oo 

*  Ordnance  and  Gunnery.     2  vols I2mo,  5  oo 

Murray's  Infantry  Drill  Regulations i8mo,  paper,  10 

Nixon's  Adjutants'  Manual 241110,  i  oo 

Peabody's  Naval  Architecture 8vo,  7  50 

*  Phelps's  Practical  Marine  Surveying 8vo,  2  50 

Powell's  Army  Officer's  Examiner 12010,  4  oo 

Sharpe's  Art  of  Subsisting  Armies  in  War i8mo,  morocco,  i  50 

*  Tupes  and  Poole's  Manual  of  Bayonet  Exercises  and    Musketry  Fencing. 

24010,  leather,  50 

*  Walke's  Lectures  on  Explosives 8vo,  4  co 

Weaver's  Military  Explosives 8vo,  3  oo 

*  Wheeler's  Siege  Operations  and  Military  Mining 8vo,  2  oo 

Winthrop's  Abridgment  of  Military  Law i2mo,  2  50 

Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

Young'*  Simple  Elements  of  Navigation i6mo,  morocco,  2  oo 


ASSAYING. 

Fletcher's  Practical  Instructions  in  Quantitative  Assaying  with  the  Blowpipe. 

i2mo,  morocco,  i  50 

Furman's  Manual  of  Practical  Assaying 8vo,  3  oo 

Lodge's  Notes  on  Assaying  and  Metallurgical  Laboratory  Experiments.  .  .  .8vo,  3  oo 

Low's  Technical  Methods  of  Ore  Analysis 8vo,  3  oo 

Miller's  Manual  of  Assaying I2mo,  i  oo 

Cyanide  Process i2mo,  i  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.) i2mo,  2  50 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Ricketts  and  Miller's  Notes  on  Assaying 8vo,  3  oo 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Ulke's  Modern  Electrolytic  Copper  Refining. 8vo,  3  oo 

Wilson's  Cyanide  Processes i2mo,  i  50 

Chlorination  Process I2mo,  i  50 


ASTRONOMY. 

Comstock's  Field  Astronomy  for  Engineers ^ 8vo,  2  50 

Craig's  Azimuth 4to,  3  50 

Doolittle's  Treatise  on  Practical  Astronomy 8vo,  4  oo 

Gore's  Elements  of  Geodesy 8vo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,  3  oo 

Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

*  Michie  and  Harlow's  Practical  Astronomy 8vo,  3  oo 

*  White's  Elements  of  Theoretical  and  Descriptive  Astronomy 12010,  2  oo 


BOTANY. 

Davenport's  Statistical  Methods,  with  Special  Reference  to  Biological  Variation. 

i6mo,  morocco,    i  25 

Thome  and  Bennett's  Structural  and  Physiological  Botany. i6mo,    2  25 

Westerrraier's  Compendium  of  General  Botany.     (Schneider.) 8vo,    2  oo 

3 


CHEMISTRY. 

Adriance's  Laboratory  Calculations  and  Specific  Gravity  Tables i2mo,  i  25 

Alexeyeff's  General  Principles  of  Organic  Synthesis.     (Matthews.) 8vo,  3  oo 

Allen's  Tables  for  Iron  Analysis 8vo,  3  oo 

Arnold's  Compendium  of  Chemistry.     (Mandel.) Small  8vo,  3  50 

Austen's  Notes  for  Chemical  Students i2mo,  i  50 

Bernadou's  Smokeless  Powder. — Nitro-cellulose,  and  Theory  of  the  Cellulose 

Molecule i2mo,  2  50 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo,  i  50 

Brush  and  Penfield's  Manual  of  Determinative  Mineralogy 8vo,  4  oo 

Claassen's  Beet-sugar  Manufacture.     (Hall  and  Rolfe.) 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.    (Eoltwcod.).  .8vo,  3  co 

Cohn's  Indicators  and  Test-papers i2mo,  2  oo 

Tests  and  Reagents 8vo,  3  oo 

Crafts's  Short  Course  in  Qualitative  Chemical  Analysis.   (Schaeffer.).  .  .  i2mo,  i  50 
Dolezalek's  Theory  of  the   Lead  Accumulator   (Storage   Battery).        (Von 

Ende.) i2mo,  2  50 

Drechsel's  Chemical  Reactions.     (Merrill.) i2mo,  i  25 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Erdmann's  Introduction  to  Chemical  Preparations.     (Dunlap.) i2mo,  i   25 

Fletcher's  Practical  Instructions  in  Quantitative  Assaying  with  the  Blowpipe. 

121110,  morocco,  i  50 

Fowler's  Sewage  Works  Analyses i2mo,  2  oo 

Fresenius's  Manual  of  Qualitative  Chemical  Analysis.     (Wells.) 8vo,  5  oo 

Manual  of  Qualitative  Chemical  Analysis.  Part  I.  Descriptive.  (Wells.)  8vo,  3  oo 
System  of    Instruction   in    Quantitative    Chemical   Analysis.      (Cohn.) 

2  vols 8vo,  12  50 

Fuertes's  Water  and  Public  Health i2mo,  i  50 

Furman's  Manual  of  Practical  Assaying 8vo,  3  oo 

*  Getman's  Exercises  in  Physical  Chemistry i2mo,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo,  i  25 

Grotenfelt's  Principles  of  Modern  Dairy  Practice.     (Woll.).  . i2mo,  2  oo 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall) i2mo,  125 

Hammarsten's  Text-book  of  Physiological  Chemistry.     (Mandel.) 8vo,  4  oo 

Helm's  Principles  of  Mathematical  Chemistry.     (Morgan.) .i2mo,  i  50 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Hind's  Inorganic  Chemistry 8vo,  3  o~ 

*  Laboratory  Manual  for  Students i2mo,  i  oo 

Holleman's  Text-book  of  Inorganic  Chemistry.     (Cooper.) 8vo,  2  50 

Text-book  of  Organic  Chemistry.     (Walker  and  Mott.) 8vo,  2  50 

*  Laboratory  Manual  of  Organic  Chemistry.     (Walker.) i2mo,  i  oo 

Hopkins's  Oil-chemists'  Handbook 8vo,  3  oo 

Jackson's  Directions  for  Laboratory  Work  in  Physiological  Chemistry.  .8vo,  i  25 

Keep's  Cast  Iron 8vo,  2  50 

Ladd's  Manual  of  Quantitative  Chemical  Analysis i2mo,  i  oo 

Landauer's  Spectrum  Analysis.     (Tingle.) 8vo,  3  oo 

*  Langworthy  and   Austen.         The   Occurrence   of  Aluminium  in  Vegetable 

Products,  Animal  Products,  and  Natural  Waters 8vo,  2  oo 

Lassar-Cohn's  Practical  Urinary  Analysis.  (Lorenz.) i2mo,  i  oo 

Application  of  Some  General  Reactions  to  Investigations  in  Organic 

Chemistry.  (Tingle.) i2mo,  i  oo 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control. 8vo,  7  50 

Lob's  Electrochemistry  of  Organic  Compounds.  (Lorenz.) 8vo,  3  oo 

Lodge's  Notes  on  Assaying  and  Metallurgical  Laboratory  Experiments 8vo,  3  oo 

Low's  Technical  Method  of  Ore  Analysis 8vo.  3  oo 

Lunge's  Tech.no-chemical  Analysis.  (Cohn.) i2mo  i  oo 

4 


*  McKay  and  Larsen's  Principles  and  Practice  of  Butter-making 8vo  i  50 

Mandel's  Handbook  for  Bio-chemical  Laboratory I2mo,  i  50 

*  Martin's  Laboratory  Guide  to  Qualitative  Analysis  with  the  Blowpipe .  .  i2mo,  60 
Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

3d  Edition,  Rewritten 8vo,  4  oo 

Examination  of  Water.     (Chemical  and  Bacteriological.) 12010,  i  25 

Matthew's  The  Textile  Fibres 8vo,  3  50 

Meyer's  Determination  of  Radicles  in  Carbon  Compounds.     (Tingle.).  .  I2mo,  i  oo 

Miller's  Manual  of  Assaying I2mo,  i  oo 

Cyanide  Process i2mo,  i  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.) .  .  .  .  I2mo,  2  50 

Mixter's  Elementary  Text-book  of  Chemistry i2mo,  i  50 

Morgan's  An  Outline  of  the  Theory  of  Solutions  and  its  Results i2mo,  i  oo 

Elements  of  Physical  Chemistry I2mo,  3  oo 

*  Physical  Chemistry  for  Electrical  Engineers i2mo,  i  50 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco,  i  50 

Mulliken's  General  Method  for  the  Identification  of  Pure  Organic  Compounds. 

Vol.  I Large  8vo,  5  oo 

O'Brine's  Laboratory  Guide  in  Chemical  Analysis 8vo,  2  oo 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Ostwald's  Conversations  on  Chemistry.     Part  One.     (Ramsey.) i2mo,  i  50 

"                   "               "           "             Part  Two.     (Turnbull.) i2mo,  200 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 

Pictet's  The  Alkaloids  and  their  Chemical  Constitution.     (Biddle.) 8vo,  5  oo 

Pinner's  Introduction  to  Organic  Chemistry.     (Austen.) I2mor  i  50 

Poole's  Calorific  Power  of  Fuels 8vo,  3  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis i2mo,  i  2$ 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Richards  and  Woodman's  Air.Water ,  and  Food  from  a  Sanitary  Standpoint.  .8vo ,  2  oo> 
Ricketts  and  Russell's  Skeleton  Notes  upon  Inorganic  Chemistry.     (Part  I. 

Non-metallic  Elements.) 8vo,  morocco,  75 

Ricketts  and  Miller's  Notes  on  Assaying '. .  .8vo,  3  oo- 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  3  50- 

Disinfection  and  the  Preservation  of  Food 8vo,  4  oo- 

Riggs's  Elementary  Manual  for  the  Chemical  Laboratory 8vo,  i  25, 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo> 

Rostoski's  Serum  Diagnosis.     (Bolduan.) I2mo,  i  oo- 

Ruddiman's  Incompatibilities  in  Prescriptions 8vo,  2  oc 

*  Whys  in  Pharmacy I2mo,  i  oo, 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo> 

Salkowski's  Physiological  and  Pathological  Chemistry.     (Orndorff.) 8vo,  2  50- 

Schimpf's  Text-book  of  Volumetric  Analysis I2mo,  2  50* 

Essentials  of  Volumetric  Analysis f i2mo,  i  25 

*  Qualitative  Chemical  Analysis 8vo,  i  25. 

Smith's  Lecture  Notes  on  Chemistry  for  Dental  Students 8vo,  2  50- 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  morocco,  3  ou> 

Handbook  for  Cane  Sugar  Manufacturers i6mo,  morocco,  3  oo» 

Stockbridge's  Rocks  and  Soils 8vo,  2  so> 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i  50- 

*  Descriptive  General  Chemistry 8vo,  3  oa- 

Treadwell's  Qualitative  Analysis.     (Hall.) 8vo,  3  oo- 

Quantitative  Analysis.     (Hall.) 8vo,  4  oo- 

Turneaure  and  Russell's  Public  Water-supplies .8vo,  5  oo> 

Van  Deventer's  Physical  Chemistry  for  Beginners.     (Boltwood.) I2mo,  i  so> 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo- 

Ware's  Beet-sugar  Manufacture  and  Refining Small  8vo,  cloth,  4  oo> 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks 8vo,  2  oo> 

5 


\Vassermann's  Immune  Sera  :  Haemolysins,  Cytotoxins,  and  Precipitins.    (Bol- 


"Weaver's  Military  Explosives  ............  ,  ......  '.'.'.'.  '.  '  '.  '.  '.  '.  '.  '.  '  '  '  '  '  '  .  .gvo,'  3  oo 

"Wehrenfennig's  Analysis  and  Softening  of  Boiler  Feed-  Water                    .8vo.  t.  oo 

Wells's  Laboratory  Guide  in  Qualitative  Chemical  Analysis  ........  .  .  .  .  .8vo,  i~  50 

Short  Course  in  Inorganic  Qualitative  Chemical  Analysis  for  Engineering 

Students  ..............................................  i2mo,  i  50 

Text-book  of  Chemical  Arithmetic  .  ...........................  12010,  i  25 

Whipple's  Microscopy  of  Drinking-water  ............................  8vo,  3  50 

Wilson's  Cyanide  Processes  ......................................  i2mo,'  i  50 

Chlorination  Process  ........................................  I2mo,  i  50 

Winton's  Microscopy  of  Vegetable  Foods  ............................  8vo,  7  =;o 

V/ulling's    Elementary    Course    in  Inorganic,  Pharmaceutical,  and  Medical 

Chemistry  ..............................................  iamo  2  oo 


CIVIL  ENGINEERING. 

BRIDGES    AND    ROOFS.       HYDRAULICS.       MATERIALS   OF    ENGINEERING. 
RAILWAY  ENGINEERING. 

Baker's  Engineers'  Surveying  Instruments i2mo,  3  oo 

Bixby's  Graphical  Computing  Table Paper  ig£  X  24!  inches.  25 

**  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Cana ..     (Postage, 

27  cents  additional.) 8vo,  3  50 

Comstock's  Field  Astronomy  for  Engineers 8vo,  2  50 

Davis's  Elevation  and  Stadia  Tables 8vo,  i  oo 

-  Elliott's  Engineering  for  Land  Drainage I2mo,  i  50 

Practical  Farm  Drainage i2mo,  i  oo 

""  *Fiebeger's  Treatise  on  Civil  Engineering 8vo,  5  oo 

Flemer's  Phototopographic  Methods  and  Instruments 8vo,  5  oo 

Folwell's  Sewerage.     (Designing  and  Maintenance.) 8vo,  3  oo 

Freitag's  Architectural  Engineering.     2d  Edition,  Rewritten 8vo,  3  50 

^French  and  Ives's  Stereotomy 8vo,  2  50 

Goodhue's  Municipal  Improvements i2mo,  i  75 

•  Goodrich's  Economic  Disposal  of  Towns'  Refuse 8vo,  3  50 

1  -Gore's  Elements  of  Geodesy 8vo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,    3  oo 

•  Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,    2  50 

^Howe's  Retaining  Walls  for  Earth i2rno,     i   25 

*  Ives's  Adjustments  of  the  Engineer's  Transit  and  Level. i6mo,  Bds.  25 

Ives  and  Hilts's  Problems  in  Surveying i6mo,  morocco,  i  50 

Johnson's  (J.  B.)  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

.Johnson's  (L.  J.)  Statics  by  Algebraic  and  Graphic  Methods 8vo,  2  oo 

Laplace's  Philosophical  Essay  on  Probabilities.    (Truscott  and  Emory.) .  i2mo,  2  oo 

JMahan's  Treatise  on  Civil  Engineering.     (1873.)     (Wood.) 8vo,  5  oo 

*  Descriptive  Geometry 8vo,  i  50 

."Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

Merriman  and  Brooks's  Handbook  for  Surveyors i6mo,  morocco,  2  oo 

INugent's  Plane  Surveying 8vo,  3  5<> 

Ogden's  Sewer  Design i2mo,  2  oo 

Parsons's  Disposal  of  Municipal  Refuse , 8vo,  2  oo 

Patton's  Treatise  on  Civil  Engineering 8vo  half  leather,  7  50 

"Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Hideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  3  50 

Siebert  and  Biggin's  Modern  Stone-cutting  and  Masonry 8vo,  i  50 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Sondericker's  Graphic  Statics,  with  Applications  to  Trusses,  Beams,  and  Arches. 

8vo,    2  oo 
6 


Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

*  Trautwine's  Civil  Engineer's  Pocket-book i6mo,  morocco,  5  oo» 

Venable's  Garbage  Crematories  in  America 8vo,  2  oo> 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo» 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo- 

Warren's  Stereotomy — Problems  in  Stone-cutting 8vo,  2  50 

Webb's  Problems  in  the  Use  and  Adjustment  of  Engineering  Instruments. 

i6mo,  morocco,  i   25 

Wilson's  Topographic  Surveying 8vo,  3  50 


BRIDGES  AND  ROOFS. 

Boiler's  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges.  .8vo,  2  oo 

*       Thames  River  Bridge 4to,  paper,  5  oo 

Burr's  Course  on  the  Stresses  in  Bridges  and  Roof  Trusses,  Arched  Ribs,  and 

Suspension  Bridges 8vo,  3  50 

Burr  and  Falk's  Influence  Lines  for  Bridge  and  Roof  Computations 8vo,  3  oo 

Design  and  Construction  of  Metallic  Bridges 8vo,    5  oa 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II Email  4to,  10  oo 

Foster's  Treatise  on  Wooden  Trestle  Bridges 4to,  5  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50- 

Greene's  Roof  Trusses 8vo,  i  25 

Bridge  Trusses 8vo,  2  50 

Arches  in  Wood,  Iron,  and  Stone 8vo,  2  50 

Howe's  Treatise  on  Arches 8vo,  4  oo 

Design  of  Simple  Roof-trusses  in  Wood  and  Steel 8vo,  2  oo> 

Symmetrical  Masonry  Arches 8vo,  2  50 

Johnson,  Bryan,  and  Turneaure's  Theory  and  Practice  in  the  Designing  of 

Modern  Framed  Structures Small  4to,  10  oo 

Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges: 

Part  I.     Stresses  in  Simple  Trusses 8vo,  2  50 

Part  II.     Graphic  Statics 8vo,  2  50 

Part  III.  Bridge  Design 8vo,  2  50- 

Part  IV.   Higher  Structures 8vo,  2  50 

Morison's  Memphis  Bridge 4to,  10  oo 

Waddell's  De  Pontibus,  a  Pocket-book  for  Bridge  Engineers.  .  i6rro,  morocco,  2  oo 

*  Specifications  for  Steel  Bridges i2mo,  50 

Wright's  Designing  of  Draw-spans.     Two  parts  in  one  volume 8vo,  3  50 


HYDRAULICS. 

Barnes's  Ice  Formation 8vo,  3  oa 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from 

an  Orifice.     (Trautwine.) 8vo,  2  oo> 

Bovey's  Treatise  on  Hydraulics 8vo,  5  oo? 

Church's  Mechanics  of  Engineering 8vo,  6  oo- 

Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels paper,  i  50 

Hydraulic  Motors 8vo,  2  oo 

Coffin's  Graphical  Solution  of  Hydraulic  Problems i6mo,  morocco,  2  50 

Flather's  Dynamometers,  and  the  Measurement  of  Power I2rco,  3  oo 

Folwell's  Water-supply  Engineering : 8vo,  4  oo 

Frizell's  Water-power 8vo,  5  oo 

7 


Fuertes's  Water  and  Public  Health ,  .121110,  i  50 

Water-filtration  Works i2mo,  2  50 

Ganguillet  and  Kutter's  General  Formula  for  the  Uniform  Flow  of  Water  in 

Rivers  and  Other  Channels.     (Hering  and  Trau twine.) 8vo,  4  oo 

Hazen's  Filtration  of  Public  Water-supply: 8vo,  3  oo 

Hazlehurst's  Towers  and  Tanks  for  Water-works 8vo,  2  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Riveted,  Metal 

Conduits 8vo.  2  oo 

Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

8vo,  4  oo 

Merriman's  Treatise  on  Hydraulics 8vo,  5  oo 

•*  Michie's  Elements  of  Analytical  Mechanics • 8vo,  4  oo 

Schuyler's   Reservoirs  for  Irrigation,   Water-power,  and   Domestic   Water- 
supply Large  8vo,  5  oo 

**  Thomas  and  Watt's  Improvement  of  Rivers      (Post.,  44c.  additional. )  4to,  6  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Wegmann's  Design  and  Construction  of  Dams 4to,  5  oo 

Water-supply  of  the  City  of  New  York  from  1658  to  1895 4to,  10  oo 

"Williams  and  Hazen's  Hydraulic  Tables 8vo,  i  50 

Wilson's  Irrigation  Engineering Small  8vo,  4  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines '. 8vo,  2  50 

Elements  of  Analytical  Mechanics 8vo,  3  oo 


MATERIALS  OF  ENGINEERING. 

Baker's  Treatise  on  Masonry  Construction 8vo,  5  oo 

Roads  and  Pavements 8vo,  5  oo 

Black's  United  States  Public  Works Oblong  4to,  5  oo 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Byrne's  Highway  Construction 8vo,  5  oo 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo,  3  oo 

Church's  Mechanics  of  Engineering , 8vo,  6  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  I Small  4to,  7  50 

=*Eckel's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Johnson's  Materials  of  Construction Large  8vo,  6  oo 

'Fowler's  Ordinary  Foundations 8vo,  3  50 

•Graves's  Forest  Mensuration 8vo,  4  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Keep's  Cast  Iron .' .  .  8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Marten's  Handbook  on  Testing  Materials.     (Henning.)     2  vols 8vo,  7  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merrill's  Stones  for  Building  and  Decqration 8vo,  5  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

Strength  of  Materials i2mo,  i  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Patton's  Practical  Treatise  on  Foundations 8vo,  5  oo 

Richardson's  Modern  Asphalt  Pavements 8vo,  3  oo 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor.,  4  oc 

*  Ries's  Clays:  Their  Occurrence,  Properties,  and  Uses 8vo,  5  oo 

Rockwell's  Roads  and  Pavements  in  France i2mo,  i  25 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines 12010,  i  oo 

-Snow's  Principal  Species  of  Wood 8vo,  3  50 


Spalding's  Hydsaulic  Cement ....  i2mo,  2  oo 

Text-book  on  Roads  and  Pavements i2mo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete.  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Materials  of  Engineering.     3  Parts 8vo,  8  oo 

Part  I.     Non-metallic  Materials  of  Engineering  and  Metallurgy 8vo,  2  oo 

Part  II      Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Thurston's  Text-book  of  the  Materials  of  Construction 8vo,  5  oo 

Tillson's  Street  Pavements  and  Paving  Materials 8vo,  4  oo 

WaddelFs  De  Pontibus     (A  Pocket-book  for  Bridge  Engineers.)-  •  i6mo,  mor.,  2  oo 

Specifications  for  Steel  Bridges.  ... i2mo,  i  25 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials,  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings;    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  oo 


RAILWAY  ENGINEERING. 

Andrew's  Handbook  for  Street  Railway  Engineers. ..  .3x5  inches,  morocco,  i  25 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brook's  Handbook  of  Street  Railroad  Location i6mo,  morocco .  i  50 

Butt's  Civil  Engineer's  Field-book i6mo,  morocco,  2  50 

Crandall's  Transition  Curve i6mo,  morocco,  i  50 

Railway  and  Other  Earthwork  Tables 8vo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book     i6mo,  morocco,  5  oo 

Dredge's  History  of  the  Pennsylvania  Railroad:    (1870) Paper,  5  oo 

*  Drinker's  Tunnelling,  Explosive  Compounds,  and  Rock  Drills. 4to,  half  mor.,  25  oo 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Godwin's  Railroad  Engineers'  Field-book  and  Explorers'  Guide.  .  .  i6mo,  mor.,  2  50 

Howard's  Transition  Curve  Field-book i6mo,  morocco,  i  50 

Hudson's  Tables  for  Calculating  the  Cubic  Contents  of  Excavations  and  Em- 
bankments  8vo,  i  oo 

Molitor  and  Beard's  Manual  for  Resident  Engineers.  s i6mo,  i  oo 

Nagle's  Field  Manual  for  Railroad  Engineers i6mo,  morocco,  3  oo 

Philbrick's  Field  Manual  for  Engineers. i6mo,  morocco,  3  oo 

Searles's  Field  Engineering i6mo,  morocco,  3  oo 

Railroad  Spiral i6mo,  morocco,  i  50 

Taylor's  Prismoidal  Formulae  and  Earthwork 8vo,  i  50 

•*  Trautwine's  Method  ot  Calculating  the  Cube  Contents  of  Excavations  and 

Embankments  by  the  Aid  of  Diagrams 8vo,  2  oo 

The  Field  Practice  of  Laying  Out  Circular  Cyrves  for  Railroads. 

i2ino,  morocco,  2  50 

Cross-section  Sheet Paper,  25 

Webb's  Railroad  Construction i6mo,  morocco,  5  oo 

Economics  of  Railroad  Construction Large  i2tno,  2  50 

Wellington's  Economic  Theory  of  the  Location  of  Railways Small  8vo-  5  oo 


DRAWING. 

Barr's  Kinematics  of  Machinery 8vo  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "                     "                    "         Abridged  Ed 8vo,  150 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

9 


Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  Engi- 
neers  Oblong  4to,  2  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo,  2  50 

Hill's  Text-book  on  Shades  and  Shadows,  and  Perspective 8vo,  2  oo 

Jamison's  Elements  of  Mechanical  Drawing 8vo,  2  50 

Advanced  Mechanical  Drawing 8vo,  2  oo 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

MacCord's  Elements  of  Descriptive  Geometry 8vo,  3  oo 

Kinematics;  or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing .* 4to,  4  oo 

Velocity  Diagrams , 8vo,  i  50 

MacLeod's  Descriptive  Geometry Small  8vo,  i  50 

*  Mahan's  Descriptive  Geometry  and  Stone-cutting 8vo,  i  50 

Industrial  Drawing.  (Thompson.) 8vo,  3  50 

Moyer's  Descriptive  Geometry 8vo,  2  oo 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (R.  S.)  Manual  of  Topographical  Drawing.  (McMillan.) 8vo,  2  50 

Smith  (A.  W.)  and  Marx's  iTachine  Design 8vo,  3  oo 

*  Titsworth's  Elements  of  Mechanical  Drawing -.Oblong  8vo,  i  25 

Warren's  Elements  of  Plane  and  Solid  Free-hand  Geometrical  Drawing.  12 mo,  i  oo 

Drafting  Instruments  and  Operations i2mo,  i  25 

Manual  of  Elementary  Projection  Drawing i2mo,  i  50 

Manual  of  Elementary  Problems  in  the  Linear  Perspective  of  Form  and 

Shadow i2mo,  i  oo 

Plane  Problems  in  Elementary  Geometry i2mo,  i  25, 

Primary  Geometry i2mo,  75 

Elements  of  Descriptive  Geometry,  Shadows,  and  Perspective 8vo,  3  50 

General  Problems  of  Shades  and  Shadows 8vo,  3  00 

Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Problems,  Theorems,  and  Examples  in  Descriptive  Geometry 8vo,  2  50 

Weisbach's    Kinematics    and    Power    of    Transmission.        (Hermann    and 

Klein.) 8vo,  5  oo 

Whelpley's  Practical  Instruction  in  the  Art  of  Letter  Engraving 12 mo,  2  oo 

Wilson's  (H.  M.)  Topographic  Surveying; 8vo,  3  50 

Wilson's  (V.  T.)  Free-hand  Perspective 8vo,  2  50 

Wilson's  (V.  T.)  Free-hand  Lettering 8vo,  i  00 

Woolf's  Elementary  Course  in  Descriptive  Geometry Large  8vo,  3  oc. 


ELECTRICITY  AND  PHYSICS. 

Anthony  and  Brackett's  Text-book  of  Physics.     (Magie.) Small  8vo,  3  oo 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements.  .  .  .  i2mo,  i  oo 

Benjamin's  History  of  Electricity 8vo,  3  oo 

Voltaic  Cell 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.     (Boltwood.).8vo,  3  oo 

*  Collins's  Manual  of  Wireless  Telegraphy i2mo,  i  50 

Morocco,  2  oo 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  i6mo,  morocco,  5  oo 

10 


Dolezalek's    Theory   of    the    Lead   Accumulator    (Storage    Battery).      (Von 

Ende.) i2mo,  2  «Jtt» 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  o^ 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo* 

Gilbert's  De  Magnete.     (Mottelay.) 8vo,  2  50 - 

Hanchett's  Alternating  Currents  Explained i2mo>  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50, 

Holman's  Precision  of  Measurements 8vo,  2  oo 

Telescopic   Mirror-scale  Method,  Adjustments,  and  Tests.  .  .  .Large  8vo,  75  , 

Kinzbrunner's  Testing  of  Continuous-current  Machines 8vo,  2  oo 

Landauer's  Spectrum  Analysis.     (Tingle.) 8vo,  3  oo 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard — Burgess.)  i2mo,  3  oo 

Lob's  Electrochemistry  of  Organic  Compounds.     (Lorenz.) 8vo,  3  oo 

*  Lyons's  Treatise  on  Electromagnetic  Phenomena.   Vols.  I.  and  II.  8vo,  each,  6  oo 

*  Michie's  Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo,  4  oo 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (Fishback.) i2mo,  2  50 

*  Parshall  and  Hobart's  Electric  Machine  Design 4to,  half  morocco,  12  50 

*  Rosenberg's  Electrical  Engineering.     (Haldane  Gee — Kinzbrunner.).  .  .8vo,  i  50 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo,  2  50 

Thurston's  Stationary  Steam-engines 8vo,  2  50- 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i   so 

Tory  and  Pitcher's  Manual  of  Laboratory  Physics Small  8vo,  2  oa 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oa 


LAW. 

*  Davis's  Elements  of  Law 8vo,  2  50.. 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

*  Sheep,  7  50 

Manual  for  Courts-martial i6mo,  morocco,  i  50 

Wait's  Engineering  and  Architectural  Jurisprudence « 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  Svo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Winthrop's  Abridgment  of  Military  Law i2mo,  2  50 . 


MANUFACTURES. 

Bernadou's  Smokeless  Powder — Nltro-oelluiose  and  Theory  of  the  Cellulose 

Molecule i2mo,  a  $<&* 

Bolland's  Iron  Founder I2mo,  a  so> 

The  Iron  Founder,"  Supplement i2mo,  2  50... 

Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  Used  in  the 

Practice  of  Moulding i2mo,  3  oo- 

Claassen's  Beet-sugar  Manufacture.    (Hall  and  Rolfe.) 8vo,  3  00* 

*  Eckel's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo~ 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Fitzgerald's  Boston  Machinist I2mo,  i  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Hopkin's  Oil-chemists'  Handbook .  .8vo,  3  oo 

Keep's  Cast  Iron 8vo,  a  50. 

11 


Xeach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control Large  8vo,  7  50 

*  McKay  and  Larsen's  Principles  and  Practice  of  Butter-making 8vo,  i  50 

Matthews's  The  Textile  Fibres 8vo,  3  50 

Metcalf  s  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Mstcalfe's  Cost  of  Manufactures — And  the  Administration  of  Workshops. 8 vo,  5  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco,  i  50 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Rice's  Concrete-block  Manufacture •  •  -8vo,  2  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Spalding's  Hydraulic  Cement I2mo,  2  oo 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  morocco,  3  oo 

Handbook  for  Cane  Sugar  Manufacturers *6mo,  morocco,  3  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Manual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 
tion  8vo,  5  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Ware's  Beet-sugar  Manufacture  and  Refining Small  8vo,  4  oo 

Weaver's  Military  Explosives 8vo,  3  oo 

West's  American  Foundry  Practice i2mo,  2  50 

Moulder's  Text-book i2mo,  2  50 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Rustless  Coatings:   Corrosion  and  Electrolysis  of  Iron  and  Steel.  .8vo,  4  oo 


MATHEMATICS. 

Baker's  Elliptic  Functions 8vo,    i  50 

*  Bass's  Elements  of  Differential  Calculus i2mo,    4  oo 

Briggs's  Elements  of  Plane  Analytic  Geometry i2mo, 

Compton's  Manual  of  Logarithmic  Computations i2mo, 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo, 

*  Dickson's  College  Algebra Large  i2mo, 

*  Introduction  to  the  Theory  of  Algebraic  Equations Large  i2mo, 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo, 

Halsted's  Elements  of  Geometry 8vo, 

Elementary  Synthetic  Geometry 8vo, 


oo 

50 
50 
50 
25 
50 
75 
50 
Rational  Geometry i2mo,  75 

*  Johnson's  (J.  B.)  Three-place  Logarithmic  Tables:   Vest-pocket  size. paper,         15 

too  copies  for    5  oo 

"*  Mounted  on  heavy  cardboard,  8X  10  inches,        25 

10  copies  for    2  oo 
Johnson's  (W   W.)  Elementary  Treatise  on  Differential  Calculus.  .Small  8vo,    3  oo 

Elementary  Treatise  on  the  Integral  Calculus Small  8vo,     i  50 

Johnson's  (W.  W.)  Curve  Tracing  in  Cartesian  Co-ordinates i2mo,     i  oo 

Johnson's  (W    W.)  Treatise  on  Ordinary  and  Partial  Differential  Equations. 

Small  8vo,     3  50 
Johnson's  (W.  W.)  Theory  of  Errors  and  the  Method  of  Least  Squares.  i2mo,     i  50 

*  Johnson's  (W   W.)  Theoretical  Mechanics I2mo,    3  oo 

Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory.) .  i2mo,    2  oo 

*  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo,    3  oo 

Trigonometry  and  Tables  published  separately Each,    2  oo 

*  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo.    i  oo 

Manning's  Irrational  Numbers  and  their  Representation  by  Sequences  and  Series 

T2mo      i  25 
1Q 


Mathematical  Monographs.     Edited  by  Mansfield  Merriman  and  Robert 

S.  Woodward Octavo,  each     i  oo 

No.  i.  History  of  Modern  Mathematics,  by  David  Eugene  Smith. 
No.  2.  Synthetic  Projective  Geometry,  by  George  Bruce  Halsted. 
No.  3.  Determinants,  by  Laenas  Gifford  Weld.  No.  4.  Hyper- 
bolic Functions,  by  James  McMahon.  No.  5.  Harmonic  Func- 
tions, by  William  E.  Byerly.  No.  6.  Grassmann's  Space  Analysis, 
by  Edward  W.  Hyde.  No.  7.  Probability  and  Theory  of  Errors, 
by  Robert  S.  Woodward.  No.  8.  Vector  Analysis  and  Quaternions, 
by  Alexander  Macfarlane.  No.  9.  Differential  Equations,  by 
William  Woolsey  Johnson.  No.  10.  The  Solution  of  Equations, 
by  Mansfield  Merriman.  No.  n.  Functions  of  a  Complex  Variable, 
by  Thomas  S.  Fiske. 

Maurer's  Technical  Mechanics .8vo,    4  oo 

Merriman's  Method  of  Least  Squares 8vo,    2  oo 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus. .  Sm.  8vo,    3  oo 

Differential  and  Integral  Calculus.     2  vols.  in  one Small  8vo,     2  50 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,    2  oo 

Trigonometry:   Analytical,  Plane,  and  Spherical i2mo,     i  oo 


MECHANICAL  ENGINEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

"Bacon's  Forge  Practice i2mo,  i  50 

Baldwin's  Steam  Heating  for  Buildings i2mo,  2  50 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "                   "                 "        Abridged  Ed 8vo,  i  50 

Benjamin's  Wrinkles  and  Recipes i2mo,  2  oo 

Carpenter's  Experimental  Engineering 8vo,  6  oo 

Heating  and  Ventilating  Buildings 8vo,  4  oo 

Cary's  Smoke  Suppression  in  Plants  using  Bituminous  Coal.     (In  Prepara- 
tion.) 

Clerk's  Gas  and  Oil  Engine Small  8vo,  4  oo 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 
gineers   Oblong  4to,  2  50 

Cromwell's  Treatise  on  Toothed  Gearing I2mo,  i  50 

Treatise  on  Belts  and  Pulleys I2mo,  i  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Fiather's  Dynamometers  and  the  Measurement  of  Power. i2mo,  3  oo 

Rope  Driving i2mo,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers * i2mo,  i  25 

Hall's  Car  Lubrication .- i2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Button's  The  Gas  Engine '. 8vo,  5  oo 

Jamison's  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kent's  Mechanical  Engineers'  Pocket-book i6mo,  morocco,  5  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Leonard's  Machine  Shop,  Tools,  and  Methods 8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.    (Pope,  Haven,  and  Dean.)  .  . 8vo,  4  oo 
MacCord's  Kinematics;   or  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing '.  .  .  .  .  4to .  4  oo 

Velocity  Diagrams 8vo,  i  50 

13 


MacFarland's  Standard  Reduction  Factors  for  Gases 8vo,  i  50 

Mahan's  Industrial  Drawing.     (Thompson.) 8vo,  3  50 

Poole's  Calorific  Power  of  Fuels ' » 8vo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richard's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism. 8vo,  3  oo 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Thurston's   Treatise   on   Friction  and   Lost   Work   in   Machinery   and   Mill 

Work.. 8vo,  3  co> 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics .  12 mo,  i  oa 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  5^ 

Weisbach's    Kinematics    and    the    Power    of    Transmission.     (Herrmann — 

Klein.).  „ 8vo,  5  oa 

Machinery  of  Transmission  and  Governors.     (Herrmann — Klein.).  .8vo,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 


MATERIALS  OP  ENGINEERING. 

*,Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.    6th  Edition. 

Reset 8vo,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Johnson's  Materials  of  Construction 8vo,  6  oo 

Keep's  Cast  Iron .  8vo,  2  50. 

Lanza's  Applied  Mechanics 8vo,  7  50. 

Martens's  Handbook  on  Testing  Materials.     (Henning.) 8vo,  7  so> 

Maurer's  Technical  Mechanics 8vo,  4  oa 

Merriman's  Mechanics  of  Materials " 8vo,  5  oo 

Strength  of  Materials i2mo,  i  oa 

Metcalf's  Steel.     A  manual  for  Steel-users i2mo,  2  oa 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish.    8vo,  3  oa 

Smith's  Materials  of  Machines i2mo,  i  oa 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  oa 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50* 

Text-book  of  the  Materials  of  Construction 8vo,  5  oo> 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials  and  an  Appendix  on 

the  Preservation  of  Timber Svo,  2  oo- 

Elements  of  Analytical  Mechanics Svo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel.,  8vo,  400. 


STEAM-ENGINES  AND  BOILERS. 

Berry's  Temperature-entropy  Diagram i2mo,  i   25 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.).  ,  .     ..i2mo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  . .  .i6mo  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy i2mo,  2  oo 


Button's  Mechanical  Engineering  of  Power  Plants. 8vo,  5  oo 

Heat  and  Heat-engines 8vo,  5  oo 

Kent's  Steam  boiler  Economy ' 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo,  i  50 

MacCord's  Slide-valves 8vo,  2  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Peabody's  Manual  of  the  Steam-engine  Indicator famo,  i  50 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors    8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines. 8vo,  5  oo 

Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Pray's  Twenty  Years  with  the  Indicator Large  8vo,  2  50 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) i2mo,  i  25 

Reagan's  Locomotives:  Simple   Compound,  and  Electric i2mo,  2  50 

Rontgen's  Principles  of  Thermodynamics.     (Du  Bois.) 8vo,  5  ot> 

Sinclair's  Locomotive  Engine  Running  and  Management I2mo,  2  oo 

•Smart's  Handbook  of  Engineering  Laboratory  Practice i2mo,  2  50 

Snow's  Steam-boiler  Practice. 8vo,  3  oo 

Spangler's  Valve-gears 8vo,  2  50 

Notes  on  Thermodynamics - i2mo,  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thomas's  Steam-turbines 8vo,  3  50 

Thurston's  Handy  Tables 8vo,  i  50 

Manual  of  the  Steam-engine 2  vols.,  8vo,  10  oo 

Part  I.     History,  Structure,  and  Theory 8vo,  6  ,00 

Part  II.     Design,  Construction,  and  Operation 8vo,  6  oo 

Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake 8vo,  5  oo 

Stationary  Steam-engines 8vo,  2  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice I2mo,  i  50 

Manual  of  Steam-boilers,  their  Designs,  Construction,  and  Operation 8vo,  5  oo 

Wehrenfenning's  Analysis  and  Softening  of  Boiler  Feed-water  (Patterson)  8vo,  4  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.) 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  oo 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines.  .  .8vo,  4  oo 


MECHANICS  AND   MACHINERY. 

Barr's  Kinematics  of  Machinery : 8vo,  2  50 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures   8vo,  7  50 

Chase's  The  Art  of  Pattern-making i2mo,  2  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Notes  and  Examples  in  Mechanics.  .  , .* 8vo,  2  oo 

Compton's  First  Lessons  in  Metal-working.  .  . i2mo,  50 

Compton  and  De  Groodt's  The  Speed  Lathe i2mo,  50 

Cromwell's  Treatise  on  Toothed  Gearing. I2mo,  50 

Treatise  on  Belts  and  Pulleys i2mo,  50 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools.  .  i2mo,  50 

Dingey's  Machinery  Pattern  Making i2mo,  oo 

Dredge's  Record  of  the  Transportation  Exhibits  Building  of  the  World's 

Columbian  Exposition  of  1893 4to  half  morocco,  5  oo 

u  Bois's  Elementary  Principles  of  Mechanics- 

Vol.      I.     Kinematics 8vo,  3  50 

Vol.    II.     Statics 8vo,  400 

Mechanics  of  Engineering.     Vol.    I.  , Small  4to,  7  50 

Vol.  II.  . Small  4to,  10  oo 

-Durley's  Kinematics  of  Machines 8vo,  4  oo 

15 


Fitzgerald's  Boston  Machinist 16010,  i  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power 12 mo,  3  oo 

Rope  Driving ^ i2mo,  2  oo 

Goss's  Locomotive  Sparks 8vo.  2  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Hall's  Car  Lubrication i2mo,  i  oo 

Holly's  Art  of  Saw  Filing i8mo,  75 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle. 

Small  8vo,  2  oo 

*  Johnson's  (W.  W.)  Theoretical  Mechanics i2mo,  3  o* 

Johnson's  (L.  J.)  Statics  by  Graphic  and  Algebraic  Methods ,  .  .  .8vo,  2  oo 

Jones's  Machine  Design: 

Part    I.     Kinematics  of  Machinery , .  .  .8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts. 8vo,  3  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Lanza's  Applied  Mechanics 8vo,  7  50 

Leonard's  Machine  Shop,  Tools,  and  Methods 8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.     (Pope,  Haven,  and  Dean.). 8vo,  4  oo 
MacCord's  Kinematics;   or.  Practical  Mechanism 8vo,  5  oo 

Velocity  Diagrams. 8vo ,  i  50 

*  Martin's  Text  Book  on  Mechanics,  Vol.  I,  Statics i2mo,  i  25 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Elements  of  Mechanics i2mo,  i  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

*  Parshall  and  Hobart's  Electric  Machine  Design 4to,  half  morocco,  12  50 

Reagan's  Locomotives     Simple,  Compound,  and  Electric i2rno,  2  50 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richards's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo,  2  50 

Sanborn's  Mechanics:  Problems .Large  i2mo,  i  50 

Schwamb  and  Merrill's  Elements  of  Mechanism.  .  , 8vo,  3  oo 

Sinclair's  Locomotive-engine  Running  and  Management I2mo,  2  oo 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  oo 

Smith's  (A.  W.)  Materials  of  Machines i2mo,  i  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Treatise  on  Friction  and  Lost  Work  in    Machinery  and    Mill 

Work 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics.  i2mo,  i  oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's  Kinematics  and  Power  of  Transmission.   (Herrmann — Klein.).  8vo,  5  oo 

Machinery  of  Transmission  and  Governors.      (Herrmann — K!ein.).8vo,  5  oo 

Wood's  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Principles  of  Elementary  Mechanics I2mo,  i  25 

Turbines 8vo,  2  50 

The  World's  Columbian  Exposition  of  1893 4to,  i  oo 


METALLURGY. 

Egleston's  Metallurgy  of  Silver,  Gold,  and  Mercury.- 

Vol.    I.     Silver 8vo,  7  50 

Vol.  II.     Gold  and  Mercury 8vo,  7  50 

Goesel's  Minerals  and  Metals:     A  Reference  Book t .  .  .  .  i6mo,  mor.  3  oo 

**  Iles's  Lead-smelting.     (Postage  9  cents  additional.).  .  , i2mo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

16 


Kunhardt's  Practice  of  Ore  Dressing  in  Europe.  . « , 8vo,  i  50 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard — ;Burgess.)i2mo.  3  oo 

Metcalf' s  Steel.     A  Manual  for  Steel-users 12010,  2  oo 

Miller's  Cyanide  Process i2mo,  i  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.).  „..  i2mo,  2  50 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Smith's  Materials  of  Machines • I2mo,  i  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  oo 

Part    II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Ulke's  Modern  Electrolytic  Copper  Refining,, 8vo,  3  oo 


MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virignia Pocket-book  form.  2  oo 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.) 8vo,  4  oo 

Chester's  Catalogue  of  Minerals 8vo,  paper,  i  oo 

Cloth,  i  25 

Dictionary  of  the  Names  of  Minerals. 8vo  3  So 

Dana's  System  of  Mineralogy Large  8vo,  half  leather  12  50 

First  Appendix  to  Dana's  New  "  System  of  Mineralogy." Large  8vo,  i  oo 

Text-book  of  Mineralogy 8vo,  4^00 

Minerals  and  How  to  Study  Them i2mo,  i  50 

Catalogue  of  American  Localities  of  Minerals Large  8vo,  i  oo 

Manual  of  Mineralogy  and  Petrography i2mo,  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo,  i  oo 

Eakle's  Mineral  Tables 8vo,  i  25 

Egleston's  Catalogue  of  Minerals  and  Synonyms 8vo,  2  50 

Goesel's  Minerals  and  Metals :     A  Reference  Book i6mo,mor..  3  oo 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall) i2mo,  i  25 

Hussak's  The  Determination  of  Rock-forming  Minerals.    ( Smith.). Small  8vo,  2  oo 

Merrill's  Non-metallic  Minerals-   Their  Occurrence  and  Uses 8vo,  4  oo 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 
Rosenbusch's   Microscopical   Physiography   of   the   Rock-making  Minerals. 

(Iddings.) *. 8vo,  5  oo 

*  Tillman's  Text-book  of  Important  Minerals  and  Rocks 8vo,  2  oo. 


MINING. 

Beard's  Ventilation  of  Mines I2mo,  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virginia. , Pocket-book  form,  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo,  i  oo 

*  Drinker's  Tunneling,  Explosive  Compounds,  and  Rock  Drills.  .4to,hf.  rnor.y  25  oo 

Eissler's  Modern  High  Explosives 8-->  4  "o 

Goesel's  Minerals  and  Metals  •     A  Reference  Book .  . i6mo,  mor.  3  oo 

Goodyear's  Coal-mines  of  the  Western  Coast  of  the  United  States i2mo,  2  50 

Ihlseng's  Manual  of  Mining 8vo,  5  oo 

**  Iles's  Lead-smelting.     (Postage  o,c.  additional.) i2mo,  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe.  .      •.  .  .  .8vo,  i  50 

Miller's  Cyanide  Process i2mo,  i  oo 

17 


'  -O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores Svo,  2  oo 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Weaver's  Military  Explosives 8vo,  3  oo 

Wilson's  Cyanide  Processes i2mo,  i  50 

Chlorination  Process i2mo,  i  50 

Hydraulic  and  Placer  Mining.' i2mo,  2  oo 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation T2mo,  125 


SANITARY  SCIENCE. 

fiashore's  Sanitation  of  a  Country  House i2mo,  i  oo 

*  Outlines  of  Practical  Sanitation I2mo,  i  25 

Folwell's  Sewerage.     (Designing,  Construction,  and  Maintenance.) 8vo,  3  oo 

Water-supply  Engineering 8vo,  4  oo 

Fowler's  Sewage  Works  Analyses i2mo,  2  oo 

Fuertes's  Water  and  Public  Health i2mo,  i  50 

Water-filtration  Works .« i2mo,  2  50 

Gerhard's  Guide  to  Sanitary  House-inspection i6mo,  i  oo 

Goodrich's  Economic  Disposal  of  Town's  Refuse Demy  8vo,  3  50 

Hazen's  Filtration  of  Public  Water-supplies 8vo,  3  oo 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control 8vo,  7  50 

Mason's  Water-supply.  (Considered  principally  from  a  Sanitary  Standpoint)  Svo,  4  oo 

Examination  of  Water.     (Chemical  and  Bacteriological.) i2mo,  i  25 

Ogden's  Sewer  Design i2mo,  2  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis i2mo,  i  25 

*  Price's  Handbook  on  Sanitation i2mo,  i  50 

Richards's  Cost  of  Food.     A  Study  in  Dietaries I2mo,  i  oo 

Costtof  Living  as  Modified  by  Sanitary  Science i2mo,  i  oc 

Cost  of  Shelter i2mo,  i  oo 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Stand- 
point  .- 8vo,  2  oo 

*  Richards  and  Williams's  The  Dietary  Computer 8vo,  i  50 

Rideal's  Sewage  and  Bacterial  Purification  of  Sewage 8vo,  3  50 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i  oo 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Winton's  Microscopy  of  Vegetable  Foods 8vo,  7  50 

Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

*  Personal  Hygiene i2mo,  i  oo 


MISCELLANEOUS. 

De  Fursac's  Manual  of  Psychiatry.     (Rosanoff  and  Collins.).  .  .  .Large  i2mo,  2  50 

Ehrlich's  Collected  Studies  on  Immunity  ( Bolduan) 8vo,  6  oo 

Emmons's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  Svo,  i  50 

ITerrel's  Popular  Treatise  on  the  Winds Svo .  4  oo 

Haines's  American  Railway  Management i2mo,  2  50 

Mott's  Fallacy  of  the  Present  Theory  of  Sound i6mo,  i  oo 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute,  1824-1894.. Small  Svo,  3  oo 

Rostoski's  Serum  Diagnosis.     (Bolduan.) i2mo ,  i  oo 

Rother ham's  Emphasized  New  Testament o Large  Svo,  3  oo 

18 


Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

The  World's  Columbian  Lxposition  of  1893 4to,  I  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i  oo 

Winslow's  Elements  of  Applied  Microscopy i2mo,  i  50 

Worcester  and  Atkinson.     Small  Hospitals,  Establishment  and  Maintenance; 

Suggestions  for  Hospital  Architecture :  Plans  for  Small  Hospital .  1 2  mo ,  125 


HEBREW  AND  CHALDEE  TEXT-BOOKS. 


Green's  Elementary  Hebrew  Grammar i amo,  i  25 

Hebrew  Chrestomathy 8vo,  2  oo 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

(Tregelles.) Small  4*0,  half  morocco,  5  oo 

Letteris's  Hebrew  Bible 8vo,  2  25 

19 


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THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
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NOV 


KOV 


1932 


AUG    231944- 


LD  21-50m-8,-32 


